A race to take on Ron DeSantis. A battle of House committee chairs. A special election that will test the political power of abortion rights.

A series of high-profile races will unfold on Tuesday in New York and Florida as the 2022 midterm primaries arrive in two of the nation’s most populous states.

Late-August elections can be unpredictable. Here are a few dynamics to watch for as results arrive on Tuesday:

Gov. Ron DeSantis of Florida is often discussed as a possible 2024 presidential contender, but first he needs to get through his re-election campaign.

Representative Charlie Crist, who served as governor from 2007 to 2011, and Nikki Fried, Florida’s agriculture commissioner, are the leading candidates in a bitter battle for the Democratic nomination to take him on.

Their contest, in which both candidates have questioned the other’s liberal bona fides, has been defined less by sharp ideological differences than by contrasts in style.

Mr. Crist, a veteran of Florida politics, is the better-funded candidate. He has cast himself as a politically seasoned unifier who emphasizes civility. And while his electoral track record is mixed, he is a well-known figure in the state. He was elected governor in 2006 as a Republican, lost a Senate race as an independent in 2010 and was defeated as a Democrat in the 2014 governor’s race. Since 2017, he has represented a St. Petersburg-area seat in Congress.

Ms. Fried, the only Democrat holding statewide office, has noted her potential as a history-maker — Florida has never had a female governor — and has tried to tap into the fury concerning the overturning of Roe v. Wade.

The winner of the primary is expected to face a difficult general election against the well-funded, well-known and nationally polarizing incumbent.

Democrats were exuberant when Kansas voters overwhelmingly rejected an effort to strip away abortion protections from their state constitution. But that was a single-issue referendum.

A special election in the Hudson Valley region of New York on Tuesday will offer an important early measure of how powerful abortion rights can be in a congressional race, as voters assess a range of other issues.

In the race for the 19th District — a battleground seat vacated by Antonio Delgado, a Democrat, when he became New York’s lieutenant governor — Pat Ryan, who serves as the executive of Ulster County, has put abortion rights at the center of his campaign.

“Choice Is on the Ballot,” one Ryan yard sign reads.

Marc Molinaro, the Republican executive of Dutchess County who ran for governor in 2018, has focused more on themes of public safety and the cost of living, moving to take advantage of voter frustration with Democratic-controlled Washington.

Both parties are watching the race as a snapshot, however imperfect, of political energy less than three months before the midterm elections.

Representatives Jerrold Nadler and Carolyn B. Maloney are veteran New York City lawmakers who occupy powerful perches in Washington. But a court-ordered redrawing of New York’s congressional district lines, combining the East and West Sides of Manhattan into a single district, ensured that at least one would not be returning to Congress, setting off a divisive and increasingly ugly Manhattan matchup.

Mr. Nadler, a fixture of the Upper West Side who leads the House Judiciary Committee, is running as a liberal lawmaker and his allies have emphasized his standing as the city’s only remaining Jewish congressman (though that could change depending on the outcome of other races).

Ms. Maloney, who has long represented an affluent East Side district, is the chair of the House Committee on Oversight and Reform, the first woman to hold that role. She had made gender a central part of her pitch, especially after the Supreme Court overturned Roe v. Wade.

And Suraj Patel, a lawyer, is running an underdog campaign, urging generational change as he competes against two lawmakers who were both elected to Congress three decades ago.

The race is not expected to be competitive in the general election, but given the stature of both Mr. Nadler and Ms. Maloney in Washington, it has drawn notable national attention.

New York is home to a pileup of primaries on Tuesday. There are House contests on Long Island and in the Syracuse area that will set the stage for competitive general election races and bitterly divisive New York City races that are revealing sharp divisions within the Democratic Party, among other battles.

The crowded race for New York’s 10th District, which under new lines includes Lower Manhattan and swaths of Brooklyn, falls into the sharp-divisions category.

Daniel S. Goldman, the chief investigator for House Democrats in the first impeachment of Donald J. Trump, has led the very limited recent polling conducted in the race, and has put at least $4 million of his own money into the contest. A number of candidates are seen as running to his left, including Carlina Rivera, a city councilwoman; Yuh-Line Niou, a state assemblywoman; and Representative Mondaire Jones, who currently represents a different district but moved to the area in the redistricting shuffle.

On the other side of the ideological spectrum, a Republican primary in Western New York has pitted the state party chairman, Nick Langworthy, against Carl Paladino, a fixture of New York Republican politics with a long history of making incendiary or racist comments. Mr. Paladino has said he has received support from a number of far-right Republicans including Representatives Marjorie Taylor Greene and Matt Gaetz (Mr. Gaetz, in Florida, faces his own primary on Tuesday.). Representative Elise Stefanik of New York, a member of House Republican leadership, is also backing Mr. Paladino.

Separately, in Oklahoma, two conservative candidates have advanced to Tuesday’s Republican runoff for the seat of retiring Senator James Inhofe: Representative Markwayne Mullin, who has former President Donald J. Trump’s endorsement and is heavily favored, and former state House Speaker T.W. Shannon.

Capturing voter attention in late August — the height of vacation season for some families, the start of school for others — can be a daunting task. Questions about turnout have injected a measure of notable uncertainty into Tuesday’s races, with the possibility that some races will end up closer than expected, or that lower-profile challengers could pull off surprising upsets.

Perhaps no New York primary is of greater national consequence than the battle for the 17th District, which includes parts of Westchester County and the Hudson Valley. Representative Sean Patrick Maloney, who leads the House Democratic campaign arm, appears to be in a strong position headed into Primary Day, but he faces a challenge from State Senator Alessandra Biaggi, a left-leaning lawmaker who defeated a powerful incumbent in 2018.