When President Trump stunned governments around the world with high tariffs, Britain was quick to strike a trade agreement with the United States that would lock in 10 percent duties on most imports while protecting key industries.

The country’s fast action appeared prudent as other deals emerged, especially one that left the European Union facing a steeper tariff rate of 15 percent on most products.

But a deep dive into the agreements suggests that the trade math is more complex.

As Mr. Trump tears up the rulebook for global trade, across-the-board rates are just a starting point. Nations face tariff rates that vary by product, complicating how governments, importers and businesses operate. There are no clear national winners and losers.

Because Britain and the European Union are neighbors, and because Britain was until 2020 part of the bloc, the deals the two economies struck are often compared. Their products already compete for American consumers, and in some cases they will now do so on a more uneven playing field. Still, a closer look at the tariffs on four specific goods — whiskey, clothing, cars and cheese — underscores how tricky it is to declare one deal better or worse.

How might the E.U. deal be better than the one Britain got? Cheese offers a good illustration.

The European Union’s trade deal includes a 15 percent across-the-board rate, except where tariffs were already higher. Britain’s 10 percent rate, by contrast, “stacks” on top of most other tariffs.

For Gouda, a popular Dutch cheese, the European Union’s 15 percent tariff applies. For English Cheddar, through, 10 percent will be added to existing tariffs, so it could face a 22 percent rate when exported to the United States.

Every pound of cheese that Neal’s Yard Dairy in London sent to the United States used to be taxed at about $1.20 on average, said David Lockwood, the company’s managing director. Now it will be about $2.

Customers will ultimately see those increases on the shop counter, he said.

Because Britain’s 10 percent tariff is stacked on existing rates, the pain is most acute in sectors that were already subjected to high levies. U.S. imports from across Europe tend to be luxury products, and the extra costs could turn off price-conscious customers.

That also applies to clothing. The European tariff on a men’s dress cotton shirt is 19.7 percent, for example. But the European Union’s 15 percent rate applies only to products that had tariffs below 15 percent, so an Italian shirt’s tax will remain 19.7 percent. A British shirt will be hit with the additional 10 percent, bringing its tariff to 29.7 percent.

“The E.U. appears to have done a better deal than the U.K. has in terms of exports for higher-duty goods,” said Paul Alger, the international business director at the UK Fashion and Textile Association.

“It’s going to be important for the U.K. government to go back to the United States to see whether a better deal can be done,” he said. But “the E.U. deal also has to be seen in the context of the other concessions that the E.U. has had to make,” he added, such as agreeing to buy more products from the United States with no tariffs.

Whiskey is an interesting category because one of its most popular varieties — Irish whiskey — faces different tariff rates depending on whether it comes from the Republic of Ireland (part of the European Union) or Northern Ireland (part of Britain).

Alcohol products from both sides of the Irish border previously faced no tariffs. Now, spirits from the south will face a 15 percent levy, while bottles from the north contend with 10 percent. British officials are pushing hard to lower whiskey tariffs during Mr. Trump’s state visit this week.

That difference is not enormous, but it puts southern producers at a slight disadvantage when the alcohol industry is already facing significant challenges as consumers drink less, in part out of health concerns.

June O’Connell is a co-founder of Skellig Six18 Distillery, a small distiller on Ireland’s southwest coast. Just this year, she introduced her product in New York, New Jersey, Maryland, Virginia and Washington, D.C.

Her whiskey is a premium product, so consumers are generally willing to pay more for it. Still, she said, competing against American whiskeys that do not have to shoulder a tariff — and northern Irish whiskeys facing lower tariffs — could make business more difficult.

“The consumer has a choice: It used to be zero-for-zero, and it was a fair fight to get their attention,” Ms. O’Connell said. “We cannot — we cannot — absorb a 15 percent tariff.”

Perhaps no tariff treatment is as complicated or as economically and politically important as that of cars. The United States is a critical market for automakers in both Britain and the European Union.

Under the new deal, the first 100,000 cars coming from Britain each year will be subject to a 10 percent tariff. That’s about the number of cars the country already exports to the United States. But it leaves British carmakers with little room for growth, because beyond the quota, tariffs will soar to 27.5 percent, the rate that the United States applied to cars from around the world this year.

For the European Union, cars are set to face a 15 percent tariff with no quota, though Europeans are still waiting for the lower rate to kick in.

But for major automakers, the reality is often far more complicated, because many of them split up production across the world.

On top of that, car parts have their own tariffs, and the Trump administration recently announced that 50 percent steel and aluminum tariffs apply to an expanded list of products, swelling a list that already included many auto components.

Guillaume Dejean, who analyzes the automobile sector for the insurance firm Allianz Trade, said the higher tariffs should ultimately be manageable for Britain and the European Union. But the timing is tough because the industry is struggling to adjust to an era of electrification and increased competition from China.

“It’s an additional burden to manage,” Mr. Dejean said. And in general, tariffs — how they will play out and whether they will change again — have created corporate unease.

“When you’re a company, what you want is certainty,” he said.

Graphics by Ani Matevosian. Illustrations by Lucia Calfapietra. Additional production by Keith Collins.