Senator Tim Scott of South Carolina opened his presidential candidacy with a story of the nation’s bitter, racist past. It is one that he tells often, of a grandfather forced from school in the third grade to pick cotton in the Jim Crow South.

A rival for the Republican nomination, Nikki Haley, speaks of the loneliness and isolation of growing up in small-town South Carolina as the child of immigrants and part of the only Indian family around. Larry Elder, a conservative commentator and long-shot presidential candidate, talks to all-white audiences about his father, a Pullman porter in the segregated South, who carried tinned fish and crackers in his pockets “because he never knew whether he’d be able to get a meal.”

Such biographical details are useful reminders of how far the G.O.P.’s candidates of color have come to reach the pinnacle of national politics, a run for the presidency. But in bolstering their own bootstrap biographies with stories of discrimination, they have put forth views about race that at times appear at odds with their view of the country — often denying the existence of a system of racism in America while describing situations that sound just like it.

“I’m living proof that America is the land of opportunity and not a land of oppression,” Mr. Scott says in a new campaign advertisement running in Iowa, though he has spoken of his grandfather’s forced illiteracy and his own experiences being pulled over by the police seven times in one year “for driving a new car.”

The clashing views of the role that race plays in America are a major theme of the 2024 election, underpinning cultural battles over “wokeness.”

Yet behind the debate over structural racism — a codified program of segregation and subjugation that suppressed minority achievement long ago and, many scholars say, has left people of color still struggling — is a secondary debate over the meaning of the stories politicians tell about themselves.

That has sometimes made the discussion of race in this presidential primary awkward but also revealing, and has underscored a central difference between the two parties. Republican candidates of color don’t see their pasts in their present, even if the two front-runners in the race for the Republican nomination, Donald J. Trump and Ron DeSantis, are elevating racial grievance to the center of conservative politics, through overt or covert appeals to white anger.

“I know Nikki and Tim — both are brilliant — but for them not to be able to make the logical jump is troubling: Systemic racism is the issue,” said Bakari Sellers, a Democratic political commentator who served with Mr. Scott and Ms. Haley in the South Carolina legislature. “For them to recount their own experiences but close their eyes to the bigger picture, it’s troubling.”

Mr. Elder, at an April gathering of evangelical Christians in West Des Moines, Iowa, spoke of his father, the Pullman porter who later became a cook in a segregated Marine Corps unit. When he returned from World War II, his father found he could not get a job in the whites-only restaurants of Chattanooga, Tenn., and struggled to find work in Los Angeles because he had no references from Tennessee.

Mr. Elder’s father even asked to cook in Los Angeles restaurants for free, just to get references, and again was refused. He ended up with two jobs scrubbing toilets.

“There was something called slavery, the K.K.K., Jim Crow — that was codified,” Mr. Elder said in an interview. “Of course there was systemic racism.”

But now?

No, he replied, recalling the election and re-election of a Black president, Barack Obama.

In the early years of the Obama presidency, talk of a post-racial society — where the color of one’s skin has no bearing on stature or success — was common. But later, an upsurge of white supremacist violence, including the massacre of Black parishioners at a Charleston church in 2015 during Mr. Obama’s second term, along with the murder of George Floyd in 2020, shattered that idealized post-racial notion for many people of color from all political persuasions.

“That’s part of the problem with Scott and Haley declaring there’s no racism,” said Andra Gillespie, a political scientist at Emory University and the author of a book on Mr. Obama’s symbolism as a Black president. “You could have argued in 2006 and 2007 that racism was waning. That’s a lot less credible today.”

Candidates of color are not the only ones who rely on bootstrap biographies to bolster their appeal. Stories of struggle, impoverished childhoods, working-class roots or ethnic identity are staples for candidates in both parties, from Abraham Lincoln to Joseph R. Biden Jr. to Mr. DeSantis and his “family of steelworkers.” But tales of racism and discrimination lend political biographies an added element of authenticity. Mr. Scott’s family story — “from cotton to Congress” — was the subject of his first campaign ad, unveiled last week.

For Republican candidates of color, whose audiences are often almost entirely white, there is another factor, according to strategists: Placing racism safely in the past and trumpeting the racial progress of their own lifetimes relieves today’s G.O.P. voters from having to confront any racial animosity in their party. That can be a soothing message to Republicans who feel defensive about the party’s racial makeup and policies.

“They’re saying this to make an overwhelmingly white Republican audience feel better about themselves,” said Stuart Stevens, a former Republican consultant who guided the party’s 2012 presidential nominee, Mitt Romney. “It’s a variation, oddly enough, of victim politics. People accuse you of being racist? ‘That’s unfair. Vote for me, therefore you’ll prove you’re not racist.’”

Under Mr. Trump, the Republican Party accommodated white nationalists in its ranks and embraced once-taboo ideas like replacement theory.

A Haley campaign spokeswoman, Chaney Denton, said: “In Nikki Haley’s experience, America is not a racist country, and she’s proud to say it. That’s fact, not strategy.” She added that “the only people who seem bothered by that” are “liberal race baiters.”

At an event on Wednesday morning sponsored by the news site Axios, Mr. Scott was pressed to describe racism that he had recently experienced, to which he had a ready response: being pulled over by police officers more than 20 times for “driving while Black,” which he said “weighs heavy on the shoulders.”

“You find yourself in a position where you’ve done nothing wrong, but you are assumed guilty before proven innocent,” Mr. Scott said on Wednesday. But he added, “Racism is embedded in the hearts of individuals.”

Many white Republicans also reject the idea that America is systemically racist.

At a Haley event in February in Iowa, Charles Strange, a retired construction worker from North Liberty, Iowa, was more apt to see systemic issues impeding white people such as himself. “Structural barriers, let’s see,” Mr. Strange said. “Here’s a structural barrier: You got quotas for Blacks for education — a structural barrier for a white person.”

“Of all the threats, there is this national loathing that has taken over our country, where people are saying America is bad or it’s rotten or it’s racist,” Ms. Haley told an Iowa crowd earlier this year. “I was the first minority female governor in the country. I am telling you America is not a racist country. It’s a blessed country.”

Many Republican voters and local officials agree.

“I’m not more racist than any Democrat, but they like to label and push that against us,” Gloria Mazza, the Republican chairwoman in Polk County, Iowa, said at a Scott event in West Des Moines.

But Black audiences, even Republican ones, are far less receptive. Such difficulties for the party were on display recently for another Republican candidate of color, the entrepreneur and author Vivek Ramaswamy.

Mr. Ramaswamy held a town-hall meeting on May 19 on the South Side of Chicago, ostensibly to discuss the migrant crisis that has divided the city. He often talks of his feelings of isolation as the son of Indian immigrants growing up in suburban Cincinnati, but says that the experience made him stronger, not a victim. He has also made eliminating affirmative action a central plank of a candidacy that centers on a critique of identity politics.

But Black voters made clear they believed strongly that systemic issues, past and present, were holding them back. The discussion kept shifting from immigration to reparations for Black Americans, mass incarceration, disinvestment in Black neighborhoods and easily accessible, high-powered weaponry promoted by the firearms industry.

“There’s all the money in the world to incarcerate us, and nothing to integrate us back into society,” Tyrone F. Muhammad, founder of the group Ex-Cons for Community and Social Change, said while looking straight at Mr. Ramaswamy, a fabulously wealthy investor. Mr. Muhammad added, “There are too many billionaires and millionaires in this country for it to look the way it looks.”

Then Cornel Darden Jr. of the Southland Black Chamber of Commerce & Industry stood to confront Mr. Ramaswamy on affirmative action. “Those laws have been in place for 70 years,” Dr. Darden said, “and we’re going to defend them.”

After months of telling largely white audiences America is not a racist society, Mr. Ramaswamy acknowledged bigotry and said race-based preferences were exacerbating it.

“I do think anti-Black racism is on the rise in America today,” Mr. Ramaswamy said. “I don’t want to throw kerosene on that.”

Maya King contributed reporting.