Tariff wars are often short. Their legacies aren’t.

President George W. Bush’s tariffs on steel products were in place for less than two years. Their impact on the economy likely lasted far longer.

Designed to protect the beleaguered but politically influential U.S. steel industry, the 2002 tariffs raised costs for companies that used steel in auto parts, metal stamping and more. Though the tariffs were rescinded the next year, the affected companies became less competitive moving forward as they tried to sell their own products abroad, said Lydia Cox, an economics professor at the University of Wisconsin-Madison.

Businesses suffered. Jobs disappeared.

“The effects were really widespread," Cox said. Her research suggests they lingered for a half-decade after Bush’s tariffs were lifted.

President Trump’s start-and-stop expansion of tariffs on major trading partners has no analog in modern history. Yet the past can still be instructive. Previous trade disputes over everything from semiconductors to lumber to chickens have sometimes dragged out for decades, rattling international markets and boosting consumer prices.

None of the presidents who pursued those policies staked his agenda on protectionism to the same extent as Trump. His measures cover an array of products: beer from Mexico, Chinese-made toys and Canadian planes.

President George W. Bush’s tariffs on steel products raised costs for many companies.

Economists fear that Trump’s approach could unleash forces that have unintended consequences extending far beyond his time in office.

“This is the biggest change to tariff policy that we’ve seen in recent history," Cox said.

Washington has historically had specific goals with previous import taxes, said Douglas Irwin, an economics professor at Dartmouth College. Reagan-era tariffs on Japanese semiconductors aimed to shield the U.S. technology sector from a daunting competitor. President Nixon ended short-lived across-the-board tariffs in 1971 soon after the export juggernauts of West Germany and Japan agreed to boost the value of their currencies.

Contrary to many trade spats of past decades, the Trump White House has offered conflicting rationales for taxing foreign goods now, a sign that the coming trade wars could be open-ended.

“The problem [today] is that it’s not clear what the ask is of other countries," Irwin said. “It’s a dramatic escalation."

The uncertainty has already dampened consumer confidence and boosted inflation expectations, with Boston Fed researchers estimating that Trump’s early tariff proposals could add 0.5 to 0.8 percentage point to core inflation depending on the response of U.S. importers.

The uncertainty has dampened consumer confidence and boosted inflation expectations.

On Wall Street, investors who previously viewed Trump’s trade rhetoric as a negotiating tactic are now grappling with the possibility that there are limited offramps ahead. The stock market has been thrashed over the past month, and the White House’s one-month exemption for many Canadian and Mexican imports on Thursday didn’t stanch the bleeding.

Trump has at times touted 25% tariffs on most goods from those countries, as well as additional 20% tariffs on China, as part of a push to stop the flow of fentanyl and migrants stateside. At other points, administration officials have portrayed import taxes as measures to boost domestic manufacturing and government revenue, objectives that economists say are at odds with each other.

Trump has likened his approach to a 19th-century paradigm that existed before international supply chains and foreign investment ballooned. In an address to Congress Tuesday, the president described tariffs as a means for protecting American jobs along with “protecting the soul of our country."

“There will be a little disturbance, but we are OK with that," he added. “It won’t be much."

Economists generally believe Trump’s trade policy was more bark than bite the first time around. Even so, tariffs on commodities and consumer goods ushered in a new era of American protectionism that the Biden administration largely extended.

In 2018, import taxes on aluminum, steel and other products aimed to bring manufacturing back home, sometimes successfully. Tariffs on washing machines created an estimated 1,800 jobs at firms like Samsung, according to a study in the American Economic Review, but they cost consumers about $1.5 billion annually, or more than $800,000 per job.

The U.S. may be the world’s largest economy, but it isn’t so big that it can force foreign suppliers to eat the cost of import taxes, said Christine McDaniel, a senior research fellow at the Mercatus Center at George Mason University.

“The U.S. absorbed well over half of those tariffs," she said. “We don’t have as much pricing power as you might think."

The Biden administration relaxed some Trump-era tariffs on imports from allied countries. But many China-focused levies remained in place, suggesting that “it is easier to ramp up tariffs than wind them down," said Jack Zhang, a political-science professor who directs the Trade War Lab at the University of Kansas.

“The lesson of protectionism is that you end up with entrenched interest groups," he said, adding that the complexity grows when governments retaliate. In countries on both sides of trade wars, protected industries “will fight like hell to keep tariffs in place."

Some U.S. trade wars have lasted decades—take the so-called Chicken Tax. After European countries slapped duties on U.S.-grown chickens in the early 1960s, President Lyndon B. Johnson retaliated with a tariff that included pickup trucks made by the likes of Volkswagen. The measure has since supported domestic manufacturing of the vehicles, analysts say, but it also limited choices and boosted price tags for car buyers.

Ripple effects can extend beyond U.S. borders. In a more than 40-year-old dispute over softwood lumber, American duties on Canadian supplies at times boosted prices so high that U.S. companies turned to imports from as far as Chile, Austria and elsewhere, said Daowei Zhang, associate dean of research at Auburn University’s College of Forestry, Wildlife and Environment.

“Not only are you paying a higher price, but also the price volatility of lumber dramatically increased," Zhang said, adding that the effects spanned U.S. construction companies, remodeling firms and homeowners. “People can’t make a plan."

Write to David Uberti at david.uberti@wsj.com