As the United States Senate debated through the night on Monday, going back and forth on President Trump’s agenda, the president himself made an announcement. “Trump Fragrances are here,” he posted on Truth Social that evening in between posts about tariff revenues and the spending bill. “They’re called ‘Victory 45-47’ because they’re all about Winning, Strength, and Success.”

The limited edition fragrances for men and women come in 3.3-ounce bottles topped with a golden statuette of the president. His autograph is displayed on the base. Each bottle costs almost $250, which is more than similarly sized luxury scents from the likes of Dior (its signature Sauvage costs $165) or Chanel (the iconic No. 5 perfume costs $110).

The Trump Fragrances add to an ever-expanding list of merchandise branded with Mr. Trump’s name and likeness, which now includes a cellphone, high-top and low-top sneakers, diamond-encrusted watches, guitars with “Make America Great Again” emblazoned across the necks and digital trading cards featuring him in an array of theatrically heroic poses, sometimes in superhero costume. The products are sold through licensing deals that, according to his financial disclosures, bring him over $7 million in income.

Victory 45-47 is the second line of presidential fragrances; the first, called Fight, Fight, Fight, was released during the campaign. That scent’s packaging featured a triumphant photo of Mr. Trump with his fist in the air, a nod to an assassination attempt against him last year. In videos online, perfume reviewers and enthusiasts noted that the actual bottle of Fight, Fight, Fight that shipped featured just a sticker logo on the bottle but that the fragrance smelled “fresh.”

Trump Fragrances “represent winning,” said Mr. Trump, standing in front of four American flags in a video on the company’s website. “Get yourself a bottle and don’t forget to grab one for your loved ones, too. They’ll thank you and they’ll even smell good.”

The Trump Fragrances website is scant on other specifics, like where the products are manufactured or what the ingredients are, and representatives for the licensing business did not respond to a request for comment. The individual product pages say that the scents are in stock and that they will “ship immediately.”

As for a description of the actual scents, the site says the men’s Victory 45-47 “blends rich, masculine notes,” while the women’s version offers a “sophisticated, subtly feminine scent.”

What, exactly, do masculinity and femininity smell like? Or what does winning even smell like?

The men’s cologne is “inoffensive, rather quiet, office-safe,” with hints of cardamom and an amber-woody finish, Elena Knezevic, the editor and co-founder of the fragrance forum Fragrantica, who got her hands on the bottles, wrote in a review of the product. And the women’s perfume smells like vanilla and gardenia with a “light gourmand strawberry touch,” Ms. Knezevic wrote. Overall, “likable and general but not at all bad.”

Generic smells are common in celebrity perfumes, Derek Guy, a men’s wear critic and writer, said in an interview. “Among people who are into perfume, there’s generally often skepticism of a celebrity perfume,” he said, because they tend to lean toward more crowd-pleasing scents in order to sell more units.

This product is not, in other words, born out of a passion for niche, interesting smells, he added.

Mr. Trump, of course, was already familiar with the world of celebrity fragrance. In 2012, he released a line called “Success.” In a GQ article about that perfume, which referred to him as a “scent enthusiast,” he was asked to elaborate on what success smelled like.

“I can’t say sweetness,” he said. “I can’t say flowery. I would say it has a good scent.”