Holiday shoppers in Atlanta talked about getting out to vote on Dec. 6, once again.

ATLANTA—The rest of the country is mostly done with the midterm elections. Votes have been counted and results are in.

But in Georgia, which is holding a run-off for its Senate race between Democratic incumbent Raphael Warnock and the Republican Herschel Walker on Dec. 6, voters need to get out and do it all again next week.

This year is different from the 2020 Senate run-off in Georgia for several reasons. For one thing, the national stakes aren’t quite so high—the Senate has already been won by the Democrats, so the makeup of Congress doesn’t hinge on Georgia alone. (That doesn’t mean that Democrats don’t want the extra seat.) There is only one run-off this year (2020 resulted in run-off contests for both Senate seats, one via special election).

And the voting electorate for this race will remain basically the same: In Georgia, voters must be registered four weeks before an election, which means residents who have turned 18 since Election Day won’t be eligible to vote on Dec. 6. (Early voting began on Nov. 28.)

But none of that means that the race isn’t just as important as the last run-off, both for the state and the country.

As people began their holiday shopping in Atlanta’s Ponce City Market, a popular food and shopping center in the city’s Old Fourth Ward neighborhood, Georgians talked about the election and why they feel compelled to show up—despite their frustrations about Georgia’s runoff rules and the fact that the run-off is, well, annoying. (People are particularly sick of the never-ceasing political ads.)

“I’ll be showing up before or after work,” said Mikayla Lucas, who works in education and was walking market’s second floor alongside employees setting up holiday décor. “It’s not ideal timing, but I have a digital day”—meaning, she doesn’t have to be in the classroom that day—“so I can and will make time to vote.”

The last run-off took place two months after the 2020 election. It attracted truly enormous levels of national attention because the entire Senate majority, under a newly elected President Biden, hinged on the win. This year, because the Senate majority has already been decided, some voters said that they were somewhat concerned that Georgia voters might be complacent and not show up to the polls a second time.

“I think people will show up, but not like they did the first time,” Telvin Debnam said on Wednesday, standing outside an Italian restaurant in the market.

“Nationally, Democrats have the Senate,” he said, which made him worried that his fellow Georgians “might not be thinking that one more seat would be helpful.” He said that Democrats shouldn’t count either Sens. Krysten Sinema or Joe Manchin to vote in their interest. Of the results of the run-off, he added, “I guess I’m not worried, but I’m worried.”

Shannon Booker also said he was worried that “people won’t come out as strongly because they aren’t looking at the bigger picture.”

“Walker is not good for Georgians, for Americans, and he’s not the person we want representing us,” he said. “Voting for someone who can barely articulate a sentence and has no knowledge of anything would be embarrassing and scary.”

He added that he couldn’t shake the feeling that Mr. Walker is a pawn for the Republican party. “In Republicans’ minds they put him out here and he’ll split the Black vote, but we know he won’t have a voice if he’s elected,” said Mr. Booker, who is Black. “He’ll just do what the people who paid for him to get there want him to do.”

The race between Walker and Warnock has gone to a run-off because no candidate won 50 percent of the votes outright. (Warnock won 49.4 percent of the vote; Walker won 48.5 percent; and the Libertarian candidate, Chase Oliver, won 2 percent.)

Symone Miller, an out-of-state visitor who was visiting Atlanta from Texas and who was also at Ponce City Market on Wednesday, said she was confounded by Georgia’s electoral process.

“Why do they need to vote twice when one person already did better than the other person?” Ms. Miller asked, noting that she hopes Georgians will show up for the runoff to “finish this.”

Ms. Miller said she has followed Georgia’s elections closely this cycle, in particular the governor’s race between Stacey Abrams and Brian Kemp and the Senate race between Warnock and Walker.

A former football champion, Walker’s campaign was characterized by shocking revelations that he had fathered “secret children” (though he made his name as a conservative figure in part by attacking the purported lack of responsibility demonstrated by absentee Black fathers) and allegations that he had pressured multiple women into having abortions, even though, as a candidate, he supports a total abortion ban with no exceptions for rape, incest, or to save the life of the patient.

Walker entered the race largely because of Donald Trump, who has continued to push his candidacy. Republicans have stood by Walker despite the news stories about abortion and secret children.

The attention on the race brought in millions and millions of dollars from both sides of the political aisle. According to NBC News, the spending on the run-off alone is expected to pale in comparison to the two Georgia Senate runoffs in 2020. That year, both parties spent nearly $500 million all together.