Jeff Mixon, leader of a Black Lives Matter group in Ohio, liked what heard in the presidential debate from Democratic nominee Hillary Clinton about addressing “implicit racism” and working to mend tattered race relations — he just doesn’t trust her to make good on her promises.

Mrs. Clinton used the buzzwords and endorsed policies popular with activists who have protested police shootings of black men. She promised federal funding for racial sensitivity training for police officers and imprisoning fewer black and Hispanic men.

“She knows exactly what to say, but whether or not you can believe it, that’s a totally different story,” said Mr. Mixon. “That’s how a lot of us feel. They talk a good game but it’s just talk.”

Republican nominee Donald Trump has tried to tap into distrust of Mrs. Clinton as he aggressively woos black voters. In the debate, Mr. Trump reminded black voters that Mrs. Clinton referred to urban youths as “superpredators” when President Bill Clinton enacted tough-on-crime policies that ultimately led to mass incarcerations of young black and Hispanic men.

The pitch in the past has failed to garner Mr. Trump significant support among black voters, according to most polls.

Mr. Mixon, a Democratic activist who frequently clashes with the party on issues of racism and party loyalty, nevertheless plans to vote for Mrs. Clinton because “Trump is so scary,” he said.

The debate crystalized the differences between Mrs. Clinton and Mr. Trump on race and policing, which has emerged as an issue with the potential to tilt outcomes in presidential swing states such as North Carolina.

Mrs. Clinton is relying on black voters to help her win in November. In a bid to shore up their support, she moved further to the side of the Black Lives Matter movement. She spoke out against systemic racism in America and in particular in the criminal justice system, giving as an example recent shootings of black men by police in Tulsa, Oklahoma, and Charlotte, North Carolina.

The former secretary of state said she recognized “implicit racism,” a concept embraced by Black Lives Matter that most people harbor subconscious racism.

“Implicit bias is a problem for everyone, not just police,” said Mrs. Clinton. “Unfortunately, too many of us in our great country jump to conclusions about each other. And therefore, I think we need all of us to be asking hard questions about, you know, why am I feeling this way?”

“But when it comes to policing, since it can have literally fatal consequences, I have said, in my first budget, we would put money into that budget to help us deal with implicit bias by retraining a lot of our police officers,” she said.

In stark contrast, Mr. Trump emphasized restoring law and order in inner-city neighborhoods where he said black residents are most affected by violent crime. He endorsed stop-and-frisk policies to get guns off the streets, although the tactic is widely viewed in black communities as racial profiling and a green light for police abuses.

The solution, he said, is creating better schools, better jobs and more opportunity in black neighborhoods, and he blamed Democratic politics for neglect.

“The African-American community has been let down by our politicians. They talk good around election time, like right now, and after the election, they said, ‘See ya later, I’ll see you in four years,’” said Mr. Trump. “The community within the inner cities has been so badly treated. They’ve been abused and used in order to get votes by Democrat politicians.”

Emory University political science professor Andra Gillespie, a race and politics scholar, said the message could resonate with black voters but Mr. Trump is the wrong messenger. Many already view him as racist or racially insensitive.

“He overestimates the extent to which he has credibility to make some of the statements he’s making,” said Ms. Gillespie.

She said his debate answers about race issues likely didn’t hurt him with his base because he did not deviate from positions he extols on the stump.

Ms. Gillespie wondered, however, how much Mrs. Clinton helped her cause in the debate.

“Even though many people think she won the debate, I don’t necessarily know how she benefits from it,” she said. “Where she could benefit from it is among African-American voters whose support was soft for her. She may have firmed up her support with that group who heard a question about race asked of the two candidates and heard very, very different answers.”

Cameron Parker, a leader of the Black Lives Matter chapter in Wilmington, North Carolina, said he is skeptical of Mrs. Clinton but is pleased that she at least acknowledges systemic racism in America.

Mr. Trump, he said, is “clueless” about racial issues.

“There isn’t that complete trust in anyone. Donald Trump had some points and some validation, like [Mrs. Clinton] has been in office all this time and why hasn’t she done something. And that’s something she had no answer for all night,” said Mr. Parker. “But you have to put your trust in something. I just feel I can trust her over him.”

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