The most important First Amendment cases of the internet era, to be heard by the Supreme Court on Monday, may turn on a single question: Do platforms like Facebook, YouTube, TikTok and X most closely resemble newspapers or shopping centers or phone companies?

The two cases arrive at the court garbed in politics, as they concern laws in Florida and Texas aimed at protecting conservative speech by forbidding leading social media sites from removing posts based on the views they express.

But the outsize question the cases present transcends ideology. It is whether tech platforms have free speech rights to make editorial judgments. Picking the apt analogy from the court’s precedents could decide the matter, but none of the available ones is a perfect fit.

If the platforms are like newspapers, they may publish what they want without government interference. If they are like private shopping centers open to the public, they may be required to let visitors say what they like. And if they are like phone companies, they must transmit everyone’s speech.

“It is not at all obvious how our existing precedents, which predate the age of the internet, should apply to large social media companies,” Justice Samuel A. Alito Jr. wrote in a 2022 dissent when one of the cases briefly reached the Supreme Court.

Supporters of the state laws say they foster free speech, giving the public access to all points of view. Opponents say the laws trample on the platforms’ own First Amendment rights and would turn them into cesspools of filth, hate and lies. One contrarian brief, from liberal professors, urged the justices to uphold the key provision of the Texas law despite the harm they said it would cause.

What is clear is that the court’s decision, expected by June, could transform the internet.

“It is difficult to overstate the importance of these cases for free speech online,” said Scott Wilkens, a lawyer with the Knight First Amendment Institute at Columbia University, which filed a friend-of-the-court brief in support of neither side in the two cases, saying each had staked out an extreme position.

The cases concern laws enacted in 2021 in Florida and Texas aimed at prohibiting major platforms from removing posts expressing conservative views. They differed in their details but were both animated by frustration on the right, notably the decisions of some platforms to bar President Donald J. Trump after the Jan. 6, 2021, attack on the Capitol.

In a statement issued when he signed the Florida bill, Gov. Ron DeSantis, a Republican, said the law was meant to promote right-leaning viewpoints. “If Big Tech censors enforce rules inconsistently, to discriminate in favor of the dominant Silicon Valley ideology, they will now be held accountable,” he said.

Gov. Greg Abbott of Texas, also a Republican, said much the same thing when he signed his state’s bill. “It is now law,” he said, “that conservative viewpoints in Texas cannot be banned on social media.”

The two trade groups that challenged the laws — NetChoice and the Computer & Communications Industry Association — said the platforms had the same First Amendment rights as conventional news outlets.

“Just as Florida may not tell The New York Times what opinion pieces to publish or Fox News what interviews to air,” the groups told the justices, “it may not tell Facebook and YouTube what content to disseminate. When it comes to disseminating speech, decisions about what messages to include and exclude are for private parties — not the government — to make.”

The states took the opposite position. The Texas law, Ken Paxton, the state’s attorney general, wrote in a brief, “just enables voluntary communication on the world’s largest telecommunications platforms between speakers who want to speak and listeners who want to listen, treating the platforms like telegraph or telephone companies.”

The two laws met different fates in the lower courts.

In the Texas case, a divided three-judge panel of the U.S. Court of Appeals for the Fifth Circuit reversed a lower court’s order blocking the state’s law.

“We reject the platforms’ attempt to extract a freewheeling censorship right from the Constitution’s free speech guarantee,” Judge Andrew S. Oldham wrote for the majority. “The platforms are not newspapers. Their censorship is not speech.”

In the Florida case, the 11th Circuit largely upheld a preliminary injunction blocking the state’s law.

“Social media platforms exercise editorial judgment that is inherently expressive,” Judge Kevin C. Newsom wrote for the panel. “When platforms choose to remove users or posts, deprioritize content in viewers’ feeds or search results, or sanction breaches of their community standards, they engage in First Amendment-protected activity.”

Forcing social media companies to transmit essentially all messages, their representatives told the justices, “would compel platforms to disseminate all sorts of objectionable viewpoints — such as Russia’s propaganda claiming that its invasion of Ukraine is justified, ISIS propaganda claiming that extremism is warranted, neo-Nazi or K.K.K. screeds denying or supporting the Holocaust, and encouraging children to engage in risky or unhealthy behavior like eating disorders.”

Supporting briefs mostly divided along the predictable lines. But there was one notable exception. To the surprise of many, some prominent liberal professors filed a brief urging the justices to uphold a key provision of the Texas law.

“There are serious, legitimate public policy concerns with the law at issue in this case,” wrote the professors, including Lawrence Lessig of Harvard, Tim Wu of Columbia and Zephyr Teachout of Fordham. “They could lead to many forms of amplified hateful speech and harmful content.”

But they added that “bad laws can make bad precedent” and urged the justices to reject the platforms’ plea to be treated as news outlets.

“To put a fine point on it: Facebook, Twitter, Instagram and TikTok are not newspapers,” the professors wrote. “They are not space-limited publications dependent on editorial discretion in choosing what topics or issues to highlight. Rather, they are platforms for widespread public expression and discourse. They are their own beast, but they are far closer to a public shopping center or a railroad than to The Manchester Union Leader.”

In an interview, Professor Teachout linked the Texas case to the Citizens United decision, which struck down a campaign finance law regulating corporate spending on First Amendment grounds.

“This case threatens to be another expansion of corporate speech rights,” she said. “It may end up in fact being a Trojan horse, because the sponsors of the legislation are so distasteful. We should be really wary of expanding corporate speech rights just because we don’t like particular laws.”

Other professors, including Richard L. Hasen of the University of California, Los Angeles, warned the justices in a brief supporting the challengers that prohibiting the platforms from deleting political posts could have grave consequences.

“Florida’s and Texas’ social media laws, if allowed to stand,” the brief said, “would thwart the ability of platforms to moderate social media posts that risk undermining U.S. democracy and fomenting violence.”

The justices will consult two key precedents in trying to determine where to draw the constitutional line in the cases to be argued Monday, Moody v. NetChoice, No. 22-277, and NetChoice v. Paxton, No. 22-555.

One of them, Pruneyard Shopping Center v. Robins from 1980, concerned a sprawling private shopping center in Campbell, Calif., whose 21 acres included 65 shops, 10 restaurants and a movie theater. It was open to the public but did not permit, as Justice William H. Rehnquist put it in his opinion for the court, “any publicly expressive activity, including the circulation of petitions, that is not directly related to its commercial purposes.”

That policy was challenged by high school students who opposed a U.N. resolution against Zionism and were stopped from handing out pamphlets and seeking signatures for a petition.

Justice Rehnquist, who would be elevated to chief justice in 1986, wrote that state constitutional provisions requiring the shopping center to allow people to engage in expressive activities on its property did not violate the center’s First Amendment rights.

In the second case, Miami Herald v. Tornillo, the Supreme Court in 1974 struck down a Florida law that would have allowed politicians a “right to reply” to newspaper articles critical of them.

The case was brought by Pat L. Tornillo, who was unhappy about colorful editorials in The Miami Herald opposing his candidacy for the Florida House of Representatives. The newspaper said Mr. Tornillo, a labor union official, had engaged in “shakedown statesmanship.”

Chief Justice Warren E. Burger, writing for a unanimous court in striking down the law, said the nation was in the middle of “vast changes.”

“In the past half century,” he wrote, “a communications revolution has seen the introduction of radio and television into our lives, the promise of a global community through the use of communications satellites and the specter of a ‘wired’ nation.”

But Chief Justice Burger concluded that “the vast accumulations of unreviewable power in the modern media empire” did not permit the government to usurp the role of editors in deciding what ought to be published.

“A responsible press is an undoubtedly desirable goal,” he wrote, “but press responsibility is not mandated by the Constitution, and like many other virtues it cannot be legislated.”