The long-running feud between former President Donald Trump and late-night host Jimmy Kimmel escalated this week after Mr. Trump referred to the comedian as “President Dementia” in a social media post and at a rally — a taunt that Mr. Kimmel later parried on air with a pointed monologue that quickly ricocheted across the internet.

The clash was the latest exchange in a yearslong back-and-forth between the two men, one that reflects the increasingly blurred lines between politics and entertainment. Mr. Trump, who has frequently criticized late-night hosts by name, has long portrayed them as partisan actors masquerading as comedians. Mr. Kimmel, for his part, has made Mr. Trump a recurring subject of satire on Jimmy Kimmel Live!.

At a recent rally, Mr. Trump dismissed Mr. Kimmel as “horrible” and suggested that if he could not surpass the host “in terms of talent,” he did not deserve the presidency. He then amplified the attack on his social media platform, branding Mr. Kimmel “President Dementia” — a phrase intended to question the host’s mental acuity while mocking his prominence in late-night television.

The insult was characteristically personal and designed for virality. Mr. Trump has often deployed derisive nicknames to frame opponents and critics, a tactic that has served as both branding device and rhetorical weapon. The strategy relies on repetition: reduce a rival to a caricature and let the shorthand circulate.

What Mr. Trump may not have anticipated was how readily Mr. Kimmel would fold the insult into his own material.

When Mr. Kimmel took the stage that evening, the audience appeared primed for a response. Rather than issue a defensive rebuttal, he leaned into the absurdity of the phrase. “President Dementia?” he said, smiling. “I didn’t know I got promoted.”

The studio erupted. Mr. Kimmel continued, noting the irony of being accused of cognitive decline by a man whose own verbal missteps and digressions have been widely documented and debated. Without raising his voice, he replayed clips of Mr. Trump’s recent remarks — moments of confusion, abrupt pivots and malapropisms — allowing the footage to serve as its own punchline.

The exchange illustrated a dynamic that has become familiar in the Trump era: an insult launched from a political stage, reframed hours later under studio lights. But this time, observers said, the contrast in tone was particularly stark. Mr. Trump’s attack was sharp and accusatory; Mr. Kimmel’s response was measured and comedic.

“He’s really fixated,” Mr. Kimmel joked at one point, suggesting that Mr. Trump’s repeated references bordered on obsession. He then added that at least the insult included the word “president,” a line that drew one of the loudest laughs of the night.

Within minutes of the broadcast, clips of the monologue spread widely on social media platforms. Supporters of Mr. Trump defended the original remark as fair retaliation against a host who frequently mocks conservatives. Admirers of Mr. Kimmel praised what they viewed as composure and timing — turning an attack into a segment that boosted ratings and online engagement.

The episode underscores how late-night television has evolved from apolitical diversion to an active arena of political commentary. Hosts now operate in a hybrid space: entertainers, cultural critics and, at times, counterpunchers in the national conversation. For politicians, the temptation to spar with them can be strong, particularly when the confrontation promises digital amplification.

Mr. Trump has shown a consistent willingness to engage in such battles. His history of branding rivals with nicknames — from primary opponents to media figures — is well established. The tactic often succeeds in dominating headlines, at least temporarily. Yet comedians, accustomed to hecklers, can be difficult targets. Their craft depends on absorbing disruption and turning it outward.

In this case, Mr. Kimmel declined to match insult with insult. Instead, he reframed the exchange as evidence of Mr. Trump’s sensitivity to criticism. “He mentioned me again,” Mr. Kimmel said, feigning surprise. “I think that’s four times this week.”

The laughter that followed suggested that, for many viewers, the comeback mattered less for its bite than for its balance. Responding to aggression with humor can shift the emotional terrain, denying the attacker the escalation he may seek.

Political analysts note that such exchanges, while entertaining, also reflect deeper tensions. Public figures increasingly treat one another as content — material to be mined, clipped and circulated. Each barb becomes both message and media strategy.

By the following morning, news outlets had replayed the duel, and commentators were debating who had gained the upper hand. Mr. Trump continued to criticize late-night hosts, while Mr. Kimmel moved on to other topics, the insult now absorbed into the churn of the news cycle.

If there was a lesson in the episode, it was less about the specific phrase than about the mechanics of attention. An insult can travel fast. A punchline can travel faster. And in a media environment where outrage often sets the pace, timing and tone can determine who ultimately controls the frame.