Just a few days after Raymond J. McGuire officially joined the New York City mayor’s race in December, a courtesy call came in from one of his Democratic rivals, Eric Adams.

Mr. Adams, who, like Mr. McGuire, is Black, offered some provocative words of wisdom.

“Being in politics is just like being in a prison yard,” Mr. Adams said, according to several people familiar with the video call. “You need to put a wall around your family because you might get shanked.”

Mr. Adams’s campaign described the sentiment as “friendly advice.” Several people in Mr. McGuire’s campaign saw it differently, characterizing it as a “veiled threat” from a front-runner trying to intimidate a new challenger.

For two years, Mr. Adams, the Brooklyn borough president, had been regarded as one of the favorites in the 2021 mayor’s race.

He was a former police officer who had nuanced views of how social justice demands could coexist with policing needs. He had broad support in Brooklyn, and had raised more than $8 million to fuel his campaign — more than anyone else in the field.

In a field of progressive rivals, he had appeared to be the leading Black moderate, representing a key city constituency. But now his stature in the race is suddenly being challenged.

Mr. McGuire, a former global head of corporate and investment banking at Citi, quickly began making inroads among political power brokers in the Black community. He hired Basil Smikle, a former executive director of the State Democratic Party, to be his campaign manager; other Black political operatives who have strong connections to Representative Gregory W. Meeks, chairman of the Queens Democratic Party, and Representative Hakeem Jeffries of Brooklyn, also signed on.

The filmmaker Spike Lee, whose brand is the borough of Brooklyn, narrated Mr. McGuire’s campaign announcement. Mr. McGuire raised $5 million in just three months, and landed the endorsement of Gwen Carr, the mother of Eric Garner, a Staten Island man whose death in 2014 after being placed in a police chokehold became a flash point for the Black Lives Matter movement.

“Eric came into this race believing that he would run a race of inevitability, not just as the borough president of Brooklyn, but the senior Black candidate in the race,” Mr. Smikle said. “Now, that’s not the case.”

Mr. McGuire and Mr. Adams have quickly become rivals, and their interactions as well as several interviews with people familiar with their relationship reveal a complicated story born at the intersection of race and class.

It’s a natural rivalry between two successful Black men from humble beginnings who took different paths — Mr. McGuire through the Ivy League and the upper echelons of Wall Street, Mr. Adams through night school and the upper ranks of the New York Police Department — to become candidates for mayor.

For Mr. Adams, the comparison is slightly irksome, adding to a perception that he might lack the polish to lead the city. He does not have the white-shoe law firm experience of Mr. Jeffries, the power broker and No. 5 House Democrat who The Washington Post once suggested was “Brooklyn’s Barack Obama,” or Mr. McGuire’s experience managing multibillion-dollar transactions.

“Coming where I come from, I think people didn’t think I’d put it together, but now I have more money to spend on a campaign than any Black person running for office in New York City’s history,” Mr. Adams said.

Four Black and Afro-Latino candidates sit among the Democratic mayoral primary’s top echelon, the most in recent memory. All talk extensively about how being Black and brown in America has affected their lives and will affect how they govern.

Initial polls suggest that Mr. Adams is running second to Andrew Yang, the former 2020 presidential candidate; Maya Wiley, a civil rights lawyer who served as Mayor Bill de Blasio’s legal counsel, is roughly in fourth place; Mr. McGuire trails behind, along with Dianne Morales, an Afro-Latina who led a nonprofit in the Bronx dedicated to eradicating poverty.

Ms. Wiley and Ms. Morales are also further behind in fund-raising; neither has yet qualified for the city’s generous matching-funds program. But while the two are competing for the progressive vote, they have largely stayed out of each other’s way, even naming the other as their second choice for mayor.

Mr. Adams and Mr. McGuire, on the other hand, seem destined for a collision course.

“I can’t remember a time where you had this many strong African-American candidates, because what normally occurs is one will emerge out of a group of several with everybody else standing down,” said Mr. Jeffries, who has not decided if he will endorse anyone in the race. “There’s no expectation that will happen in this particular instance.”

Evan Thies, a spokesman for Mr. Adams, described the prison yard remarks during the video call as “nothing more than friendly advice about the intense world of city politics.”

“To infer otherwise,” he continued, “is an example of the kind of bias that Eric has been fighting his entire life.”

But Mr. Adams’s video call in December was not the only time he had directed criticism at Mr. McGuire. At a forum in January, Mr. Adams said that he “didn’t go to the Hamptons” when the pandemic struck New York City — an apparent jab at Mr. McGuire, who said he had spent a total of three weeks in the Hamptons with his family last summer.

The remarks were similar to ones Mr. Adams made at a virtual meeting with the Fred Wilson Democratic Club in Queens in December, when he said that he didn’t attend Harvard and didn’t need to introduce himself to voters.

Mr. McGuire, who left his job at Citigroupto run for mayor, has also sought to draw a contrast with his rivals, often saying that he has not been “termed out” and isn’t “looking for a promotion” — a likely reference to Mr. Adams and Scott M. Stringer, the city comptroller, who are both barred by city law from running for third consecutive terms.

As moderate Democrats, Mr. Adams and McGuire share several policy positions. Both are in favor of revamping Police Department protocols, but have not called for defunding the police. Mr. Adams was originally in favor of a plan from Mr. de Blasio to scrap the Specialized High Schools Admissions Test, but changed his position and now believes — as Mr. McGuire does — that the test should not be the only criteria for admission.

One area where they differ is on taxing the wealthy. Mr. Adams wants to increase taxes on those who earn more than $5 million per year for two years, and use the money to help the city recover from the pandemic. Mr. McGuire, who has business community support, has said that wealthy New Yorkers such as himself should pay their fair share but also believes that the city has to grow itself out of its financial deficit.

The Black electorate in New York City is diverse, made up of Caribbean-Americans and African-Americans; of native New Yorkers, immigrants and transplants from other states. In the 2013 mayoral race, Mr. de Blasio won partly because of his enormous popularity among Black voters: Ninety-six percent of Black New Yorkers voted for him, according to exit polls, a higher percentage than David N. Dinkins captured in 1989 when he was elected as the city’s first Black mayor.

In the 2013 Democratic primary, Mr. de Blasio garnered 18,000 more votes in predominantly African-American neighborhoods than a Black rival, the former city comptroller, William C. Thompson Jr., largely based on how they proposed handling the policing tactic of stop and frisk.

Given the financial difficulty wrought by the pandemic, Mr. McGuire’s financial pedigree may help with voters in places like central Brooklyn and southeast Queens, said Anthony D. Andrews Jr., the leader of the Fred Wilson Democratic Club in Southeast Queens. He said that residents there are concerned about the city’s unequal property tax system and whether government jobs will be eliminated.

“Some people will say the complexity of the city requires someone with a certain kind of education to be able to manage a $100 billion enterprise,” said Marc H. Morial, the former mayor of New Orleans and current president of the National Urban League, who knows both men. “But there may be other people who say, ‘Is that guy in touch with me? Does he know my pain?’”

Mr. McGuire, who was urged by business leaders to run for mayor, has tried to accentuate his rise from a modest upbringing in his stump speeches. He was so poor growing up, he has said, that he washed and reused aluminum foil, and pressed scraps of soap together until they formed a bar.

Having never met his father, Mr. McGuire was raised by his mother and his grandparents in a house full of foster siblings on the “wrong side of the tracks” in Dayton, Ohio. He found his way to a prestigious private school, went on to earn three degrees at Harvard, and became one of the highest-ranking Black executives on Wall Street, a mentor to young people of color and a behind-the-scenes patron of Black causes.

“A Black man who grew up the way I grew up, I know exactly what they are going through,” Mr. McGuire said. “I know about the struggle.”

Mr. Adams has touched on similar hardships of his youth, recalling at mayoral forums that neighbors used to leave food and clothes outside his family’s home. He said he first took an interest in becoming an officer after he was beaten by the police as a teenager.

Mr. Adams worked his way up the ranks of the Police Department and founded 100 Blacks in Law Enforcement Who Care, an advocacy group to confront institutional racism in the profession. He attended night school to attain a bachelor’s and a master’s degree, and has taken to saying that he will be a “blue-collar” mayor.

“I’m not fancy,” Mr. Adams said at a recent Queens County Democratic Party forum. “I was a dishwasher. I worked in a mailroom.”

“Acknowledging the problems Black people face,” Mr. Adams said, “is different from understanding the problems.”

Mr. Adams was recently endorsed by four wrongfully convicted men, dozens of ministers and leaders from the city’s African community. Four Black City Council members, including I. Daneek Miller, co-chairman of the Black, Latino and Asian Caucus, have also endorsed Mr. Adams.

Of Mr. Adams’s supporters on the Council, another caucus member, Laurie A. Cumbo, the majority leader, has been among the most forceful in her criticism of Mr. McGuire.

At a mayoral forum, Ms. Cumbo, who represents a Brooklyn district, questioned whether Mr. McGuire had made a “visible commitment to the community” before deciding to run for mayor. She criticized his charitable work in the art world as too “highbrow,” and said that he should make sure that his campaign was “more in alignment with the people.”

Not long after, Mr. Adams and Mr. McGuire appeared at a Martin Luther King’s Birthday celebration in Harlem. Hoping to keep the peace, Mr. Adams pulled Mr. McGuire aside and told him that Ms. Cumbo’s comments were not coordinated with his campaign.

Ms. Cumbo was not interested in peacemaking.

“Ray McGuire is running a ‘Hello, my name is Ray McGuire’ kind of campaign,” she said. “Eric is running a ‘Hey sis, I just saw your mom yesterday getting the vaccine’ kind of campaign.”