Donald Trump has often been described as the second coming of P. T. Barnum, the legendary 19th-century showman. Biographers, academics and journalists have embraced this idea, as have members of Mr. Trump’s family. “He is P. T. Barnum,” his sister once said. With a movie opening on Wednesday that is loosely inspired by Barnum’s life — “The Greatest Showman,” starring Hugh Jackman — we’re likely to hear these comparisons again.

Please: Barnum would be appalled by Mr. Trump. While they share some superficial similarities, it’s the differences that stand out.

Phineas Taylor Barnum is a figure frequently invoked but rarely understood. He amassed a fortune promoting a bewildering range of popular entertainments: an elderly slave masquerading as George Washington’s nursemaid; a gifted Swedish opera singer, Jenny Lind, whom he turned into an international superstar; a half-monkey, half-fish masterpiece of taxidermy that he advertised as the FeeJee Mermaid; and other attractions, dubious and genuine. Many of these he exhibited at his American Museum in Lower Manhattan. Later, he took the show on the road, touring the world with his famous circus and sideshows.

Barnum’s hyperbole, his willingness to bend the truth when promoting his entertainments, his artful manipulation of the press, never mind his participation in outright hoaxes, invite comparisons with Mr. Trump. Likewise, Barnum’s fondness for living large — he built a garish Moorish mansion he called “Iranistan” — calls to mind Mr. Trump’s gilded excesses. Both men became teetotalers; both went bankrupt, only to claw their way back to the top. And then, of course, there’s Barnum’s famous saying: “There’s a sucker born every minute.”