There is no question older Americans are worried that any health care overhaul may cut end up cutting their benefits, even if the worst of those fears are being stoked by misinformation.

What may be more puzzling is how much confusion there is among Medicare recipients about what the program is — as evident in the variants of “Keep government out of Medicare!” that have been shouted at town hall meetings.

Perhaps the outbursts should not have come as a surprise. In 2003, the Kaiser Family Foundation and Harvard School of Public Health conducted a nationwide poll in which more than 1,400 adults, including 441 persons 65 and older, were asked, “To the best of your knowledge, is Medicare primarily a federal government program, a state government program or a private insurance program?”

The majority of seniors — 78 percent — identified Medicare as a federal program. The rest were uncertain, or thought the coverage was provided by private insurance or their states.

How can so many fail to understand that Medicare is a federal program? Experts cite several reasons.

First, seniors don’t get all their coverage for free; they are paying into the system. They have to pay 25 percent of the premium for Medicare Part B, which covers doctor bills and outpatient procedures. These payments are deducted automatically from Social Security checks.

Perhaps more confusing, seniors make other payments directly to insurance companies. Prescription drug coverage, known as Medicare Part D, is administered by private insurers (though three-quarters of the cost is borne by the government). Many recipients also turn to insurance companies for so-called Medigap policies to cover things like deductibles that Medicare won’t pay for. In those cases, part of the patchwork of coverage really is private.

In other ways, too, Medicare can feel like a private program. Enrollees choose their doctors, present their Medicare cards and let their physicians’ offices handle the paperwork. But they can still receive bills for uncovered fees from the doctors.

“The perception is that it’s between the doctor, the lab and the patient,” said Dr. Cheryl Phillips, president of the American Geriatrics Society. “It feels like a private choice versus something that’s externally reviewed. Most people are kept separate from how coverage and payment decisions are made.”

And when statements of Medicare benefits do arrive, they resemble traditional insurance statements. They note the dates of service, services provided, the amount charged, any deductibles, the portion that’s not covered and the all-important amount “you may be billed.” Granted, the notices are printed on C.M.S. letterhead. But how many people know what C.M.S. stands for? (For the very observant or those with magnifying glasses or youthful eyes, the answer sits on the page in minuscule type — the federal Centers for Medicare & Medicaid Services.)

Finally, about 20 percent of seniors actually do belong to private plans. These so-called Medicare Advantage plans cost more than traditional Medicare plans, and in many of these plans, enrollees must pay premiums directly to insurance companies. True, they are heavily subsidized by the government. But that may not be evident to seniors whose primary contact with the system is through a private insurer.

A pattern of confusion regarding government-run health programs is not atypical, said Susan Dentzer, editor-in-chief of the journal Health Affairs, in an e-mail interview.

“A lot of people who are on Medicaid, or whose kids are on SChip, are actually enrolled with private managed care organizations that have contracts with states to provide and manage Medicaid or SChip benefits,” she said. (SChip, pronounced ESS-chip, is short for State Children’s Health Insurance Program.)

“When the Census Bureau does its annual surveys asking what type of coverage people have, some of these people say they have private coverage, when in fact they don’t,” she added. “It’s one of the reasons why the Census Bureau survey is thought to undercount the actual number of people on Medicaid.”