ATLANTA — Stacey Abrams ended her Democratic bid to become governor of Georgia on Friday, acknowledging that she did not have the votes to beat her Republican rival, Brian Kemp, but sounding a defiant note by declaring that an “erosion of our democracy” had kept many of her backers from the polls.

The narrow defeat of Ms. Abrams, who would have become the first black woman to be elected governor anywhere in the United States, as well as the apparent loss of Andrew Gillum, who sought to become Florida’s first black governor, at once illuminated the vestiges of Southern history and demonstrated how demographic changes have taken hold across the region and begun to reshape its politics.

The two candidates ran as unabashed liberals and their strong showings in two pivotal states where Democrats have lately struggled is likely to keep the debate going within the Democratic Party over the best strategy for making gains in 2020. There is significant internal disagreement over which candidates the party ought to put forward and how they should run.

The race between Ms. Abrams and Mr. Kemp pitted two versions of Georgia against one another. Ms. Abrams, 44, represented the diverse future of the state and its capital, Atlanta, home to black colleges and a hub of black political power. Mr. Kemp, 55, who bragged he had a pickup truck big enough to “round up criminal illegals,” played to the state’s rural voters and linked himself with President Trump. In the end, it was enough to allow the Republican Party to maintain its grip on power in Georgia, which has not elected a Democrat as governor since 1998.