To left-leaning Democrats, Stacey Abrams, who is making her second run for Georgia governor, is a superstar: a nationally recognized voting-rights champion, a symbol of her state’s changing demographics, and a political visionary who registered and mobilized tens of thousands of new voters — the kind of grass-roots organizing that progressives have long preached.

“I don’t think anyone could call Stacey Abrams a moderate,” said Aimee Allison, the founder of She the People, a progressive advocacy group for women of color.

Moderates would beg to differ. They see Ms. Abrams as an ally for rejecting left-wing policies that center-left Democrats have spurned, like “Medicare for all,” the Green New Deal to combat climate change and the defunding of law enforcement in response to police violence.

“I don’t know that anybody in the party can say, ‘She’s one of us,’” said Matt Bennett, a founder of Third Way, the center-left group. “We can’t pretend she’s a moderate,” he added. “But the progressives can’t say she’s a progressive and not a moderate. We’re both kind of right.”

The question of how to define Ms. Abrams, 48, the presumptive Democratic standard-bearer in one of the most high-profile races of 2022, takes on new urgency amid the current landscape of the party.

Moderates and progressives sparred in Washington throughout 2021, frustrating a White House struggling to achieve consensus on its priorities and continuing an ideological debate that has raged in the party for years. There is also thirst for new blood across the party, considering the advanced ages of President Biden, congressional leaders, and leading progressives like Senator Bernie Sanders of Vermont and Senator Elizabeth Warren of Massachusetts.

On a local level, whether Ms. Abrams maintains credibility with both Democratic wings may determine how well she can withstand Republican attacks. Those close to her campaign say they expect an extremely close race, and that the key is holding the suburban moderates who supported her in 2018 while exciting enough of the new Georgia voters who have registered since that election.

Republicans in Georgia — who await Ms. Abrams in the general election — are eager to denounce her as a left-wing radical out of place in a state that was a G.O.P. stronghold until it narrowly tipped into the Democratic column in 2020. Gov. Brian Kemp, who faces a fierce primary challenge in May from former Senator David Perdue, who has the support of former President Donald J. Trump, has released five digital advertisements attacking Ms. Abrams since she announced her campaign on Dec. 1.

“Stacey Abrams’ far left agenda has no place in Georgia,” one warns ominously.

But a review of Ms. Abrams’s policy statements and television advertisements, and interviews with political figures who have known her for years, reveal a leader who has carefully calibrated her positions, making a point to avoid drifting into one Democratic lane or another.

Her allies say the fluidity is an asset, and highlights how policy is only one way that voters choose which candidate to rally behind. Racial representation and the unique political context of the American South are also factors in whether a candidate can credibly claim progressive bona fides, they argue.

Steve Phillips, an early supporter and prominent progressive Democratic donor, said Ms. Abrams’s political strategy was progressive, even if her policy positions were more moderate.

“It’s hard for white progressives to be too critical of someone who is so strongly and fiercely unapologetically Black and female,” he said. “Her authenticity comes from the sectors that are the core parts of the progressive base.”

Ms. Abrams’s approach does carry risks. In the 2020 Democratic presidential primary race, several candidates who sought to straddle the line between moderate and progressive policies lost the trust of significant numbers of voters in both camps, as activists pushed for firm commitments on issues like health care, climate change, expanding the Supreme Court and reparations for descendants of enslaved people.

At times, Ms. Abrams has used her perch to speak out against progressive causes and defend the Democratic establishment. She said attempts to defund police departments after the murder of George Floyd were creating a “false choice” and said departments should be reformed instead.

On health care, she has focused on expanding Medicaid rather than supporting a single-payer system. And in 2020, a think tank founded by Ms. Abrams released a climate plan focused on the South that embraced efforts to incentivize renewable energy but stopped short of the ambitious goals pushed by progressive activists and lawmakers like Representative Alexandria Ocasio-Cortez of New York.

But Ben Jealous, a former Democratic candidate for governor of Maryland who leads the progressive group People for the American Way, said progressives should trust Ms. Abrams just the same. “The Green New Deal is designed for the industrialized unionized North,” he said. “And you’ve got to translate that into Southern.” He added, “She does that.”

Several of Ms. Abrams’s allies welcomed an examination of her policy record, arguing that characterizing her as a progressive only fueled Republican attacks.

Ms. Abrams declined to be interviewed for this article. Asked how she defined herself ideologically, a spokesman, Seth Bringman, said she “defines herself by her values and her ability to deliver results for the common good by navigating disparate groups and ideologies.”

“She’s unwavering in her support for unions, and she worked with anti-union corporations to stop discrimination against the L.G.B.T.Q. community,” he added. “She’s unapologetically pro-choice, and she coordinated with anti-choice legislators to pass criminal justice reform. She’s a capitalist who supports regulation and believes we can fight poverty while praising success.”

Such pragmatism has encouraged some moderates — including Georgians who served with Ms. Abrams in the State Capitol — to compare her to other center-left national figures who had credibility among the grass-roots base, like Presidents Barack Obama and Bill Clinton. Mr. Bennett, a co-founder of Third Way, said Ms. Abrams had demonstrated that she “wasn’t going to be pushed around by anybody in the party, from the center or from the left.”

He added, “That independence has made her a very viable candidate.”

Carolyn Hugley, a Georgia state representative who has known Ms. Abrams since 2011, said she had always sought to be seen as a “doer” and an organizer. As minority leader, Ms. Abrams, a budget wonk, aligned with Tea Party members and some religious groups to oppose a Republican tax reform bill.

“If you had asked me 10 years ago if voting rights was what she was going to be known for, I would probably say no,” Ms. Hugley said.

In Georgia, Ms. Abrams became known for her willingness to work with anyone, even if it led to a backlash. In 2011, she lent bipartisan credibility to an effort by Gov. Nathan Deal, a Republican, to restructure the state’s scholarship program for low-income students. Several Democrats criticized her decision to stand with him at a news conference, saying it gave a gift to an incumbent who had sought to shrink the program and was an example of Ms. Abrams’s putting her own ambitions above the party’s long-term interests.

“It got misinterpreted,” said DuBose Porter, a former chairman of the Georgia Democratic Party. “But the real Stacey Abrams will always come through. And that real Stacey Abrams is somebody that cares about the issues.”

Mr. Jealous, of People for the American Way, said he recalled Ms. Abrams encouraging him to reach out to Newt Gingrich, the Georgia Republican and former House speaker, to build cross-aisle support for reforming the state’s prisons.

This campaign cycle, even Ms. Abrams’s supporters concede that the intensifying spotlight could test her political talent anew. The prospect that she could become the first Black woman in the country to be elected governor has already renewed whispers about her possible presidential ambitions.

Unlike in 2018, when Ms. Abrams was not yet a national figure, or during Mr. Biden’s vice-presidential search, in which she was considered a long shot, she enters the 2022 race as a marquee name on the Democratic roster — and a prime target for Republicans.

The Virginia governor’s race offered a preview of what Ms. Abrams could face, with Democrats on the defensive and Republicans pummeling them over Mr. Biden’s vaccine mandates, how schools teach about racism and the removal of Confederate statues.

Ms. Abrams rallied Virginia Democrats behind the Democratic candidate, former Gov. Terry McAuliffe, in the days before the election — a testament to her standing in the party. By contrast, Ms. Ocasio-Cortez said she and other progressives were told to stay away.

When announcing her candidacy in December, Ms. Abrams stuck to local themes, highlighting her work during the pandemic and her efforts to expand Medicaid access in Georgia. In the 2018 governor’s race, she did not run an ad about race or voting rights, according to a list her aides provided.

Last month, during an online campaign event with more than 350 supporters on the theme of “One Georgia,” Ms. Abrams steered clear of policy specifics and hot-button cultural conversations, focusing instead on issues like the coronavirus and education — and on her Republican opponents.

“When people ask what’s the biggest difference between me and the current governor, it’s that I like Georgians,” Ms. Abrams said. “I like all of them. The ones who agree with me and the ones who do not.”

As much as Democrats may want to label her, Mr. Jealous advised against it, citing two lessons he learned about Ms. Abrams when they first met as 19-year-old college activists. The first: She would not be pushed to go anywhere she was not comfortable. The second: “Never speak after her,” he said.

Mr. Phillips, the Democratic donor, said he was confident that the war between moderates and progressives would not affect Ms. Abrams in 2022.

When, then, would it matter?

“If and when she runs for president,” he said.