States and major cities across the country have imposed the most extensive restrictions on business and social gatherings since widespread lockdowns during the spring, in hopes of preventing a further surge in Covid-19 cases over the winter holidays.

Even as Pfizer Inc. and Moderna Inc. deliver the first doses of the coronavirus vaccine, officials are pleading with a weary—and sometimes defiant—public to avoid the kinds of gatherings and travel that helped drive new cases to record levels nationally after Thanksgiving.

“We can’t let up now. We need to continue all our efforts to stop the spread of Covid-19 in a very vulnerable time,” said Dr. Rachel Levine, secretary of health in Pennsylvania, where Democratic Gov. Tom Wolf on Dec. 10 ordered places such as movie theaters and bowling alleys to close through Jan. 4, and limited restaurants to takeout service, prompting some to stay open in resistance.

Nearly 85 million Americans are expected to travel from Dec. 23 through Jan. 3, off at least 29% from last year, according to an estimate by AAA. In states across the country, small businesses and restaurants are being hit with de facto lockdowns because of occupancy limits or restrictions on dining. At the same time, big-box retailers have been permitted to stay open, in part because their large stores allow for social distancing, prompting resentment from small-business owners.

Brenda Reid, owner of Brenda’s Family Restaurant in Mill Run, Pa., said she had no choice but to defy the state’s shutdown of indoor dining, saying she and her eight employees rely on the income. Ms. Reid added that she drained most of her savings during the five-week spring shutdown.

If she closed now, Ms. Reid said, she probably would need to shut the restaurant permanently and find a new job. “At 68 years old, that’s a little hard,” she said.

In the spring, all but a handful of states issued stay-at-home orders that ground nonessential economic activity to a halt. At the time, states were short of ventilators, testing capacity and personal protective equipment for health-care workers, and lacked treatments for the new virus. Those broad orders slowed the rate of infection and bought time for hospitals to catch up. Now, as case numbers surge, most states are clamping down on activities that help the virus spread while trying to avoid a complete shutdown of the economy.

North Carolina, which currently has a curfew on nonessential activities, issued its initial stay-at-home order on March 27.

“We didn’t know how fast the virus was spreading, what we were really dealing with,” said Dr. Mandy Cohen, North Carolina’s secretary of health and human services. “More importantly, we didn’t have our response capabilities up and mature.”

After the spring shutdowns, some states dropped many restrictions, while others eased back.