There is just one federal health law, but the way Americans experience the debut of its main provisions on Oct. 1 will vary widely depending on where they live.

Every state, whether it supports the law or not, will have a health-insurance exchange where people will shop for coverage—the health overhaul’s centerpiece.

But some states are running their own exchanges, while others are letting the federal government handle that task. Some are pushing ahead with the biggest expansion of Medicaid—the federal-state program for the poor—since its creation in the 1960s. Others aren’t extending local eligibility rules for Medicaid. Some are giving generous funds to “navigators” who are supposed to help people sign up. Elsewhere, navigators face restrictions.

“Your prices, your consumer experience will differ dramatically across states or even regions in states,” said Joel Ario, managing director at Manatt Health Solutions, a New York-based health-care consulting practice. Rural areas will likely have fewer insurer choices than urban areas, where insurers are competing more vigorously for new customers.

The divergences could make it harder to judge the law’s success, at least initially. With the health law, President Barack Obama envisioned expanding medical coverage for most of the 48 million people who currently don’t have it and placed confidence in governments to run the system smoothly. Critics called his plan a government takeover of health care that would result in bureaucracy run amok and higher costs. After coverage begins Jan. 1, gauging which of those scenarios will be closer to the truth could vary depending on the conditions in each area.

In general, the states that declined to run their own exchanges are the ones where conservative legislators and voters have been most hostile to “Obamacare.” Many of those states also have had historically tight eligibility for Medicaid and are generally declining to expand it now. And they are also the states most likely to have added restrictions on navigators.

Not all the differences fall along a red state-blue state divide. Both Kentucky and Missouri voted against Mr. Obama, but Kentucky is running its own exchange and using state employees to encourage enrollment, while Missouri is relying on the federal government’s exchange and barring state employees from helping.

The price of insurance policies available on the exchanges varies by area—and just as importantly, the perception of the prices is likely to be different. Some states have long had tight restrictions on the kind of policies that can be sold to individuals and small businesses, resulting in relatively higher prices. People in those states aren’t likely to see big premium jumps. In states that left insurers with a freer hand, some people face greater price increases.

In Atlanta, before Georgia’s new federally run health exchange kicks off, the cheapest plan available now has a monthly base rate of $43 for a healthy 30-year-old male nonsmoker, reflecting the state’s light regulation. The median plan starts at $108 a month, according to a federal database of plans. Next year, that same customer will likely have to pay at least $188 a month, although some lower-income people could get subsidies toward premium costs.

Under the new system, insurers must accept all comers and can’t charge sick people more. Currently, insurers in some states are allowed to offer healthy people skimpy plans with low rates, but those will go away when new federal requirements kick in this fall.

“I was always skeptical of Obamacare,” Georgia Insurance Commissioner Ralph Hudgens, a Republican, said in a statement. “But I never imagined that it would lead to rates being doubled or tripled. Increases of this magnitude will make coverage less affordable and increase the number of uninsured in Georgia.” Nationwide, people who forgo coverage next year face a fine of at least $95.

By contrast, health insurance has long cost more in New York, in part because the state has barred insurers from rejecting customers over pre-existing conditions. In the new health exchanges, the lowest-cost plan for a person living in Albany, regardless of age or tobacco usage, will be $237 a month, according to the state insurance regulator.

“These plans and rates deliver on the promise that the exchange will offer quality health insurance coverage at a price that works for New Yorkers,” said the executive director of the New York Health Benefit Exchange, Donna Frescatore, who was appointed by Democratic Gov. Andrew Cuomo.