When political candidates speak, they are often addressing several audiences at once, and their words can have different meanings for each. When Hillary Clinton talked about race during her debate Monday night against Donald J. Trump, she delivered a subtle and powerful message to black voters, speaking to them not only in the substance of what she said, but in her carefully chosen language.

Mrs. Clinton has been viewed with skepticism by some black activists since the 1990s, when she called for harsh penalties for teenage gang members, whom she termed “super-predators.” But throughout the 90-minute forum Monday night, she showed her determination to persuade large numbers of black voters to support her in November by adopting the lexicon that has been embraced by a new generation of young black activists and liberal whites.

Mrs. Clinton’s expressions set off a range of reactions, from relief to delight, to accusations of cynical political maneuvering. But there was near universal agreement that her use of the language of the racial justice movement signaled a significant moment for both the candidate and the cause. Here is a look at what Mrs. Clinton said and what it meant to certain viewers.

‘Systemic Racism’

“We’ve got to address the systemic racism in our criminal justice system.”

A central demand of Black Lives Matter activists has been the recognition of the role that systems — such as the funding of schools through property taxes — play in fostering racial inequality.