(CNN) President Donald Trump sowed more confusion over coronavirus testing and treatment in his Wednesday night Oval Office address , when he indicated that coronavirus patients could have treatment -- which could run into thousands of dollars for those seriously ill -- at no charge.

"Earlier this week, I met with the leaders of health insurance industry who have agreed to waive all co-payments for coronavirus treatments, extend insurance coverage to these treatments and to prevent surprise medical billing," he said.

Dr. Robert Redfield, director of the US Centers for Disease Control and Prevention, further muddied the waters on Thursday. He testified at a House Oversight Committee hearing that both the cost of testing and treatment will be covered.

This is not the case. Many insurers have said they will pick up the cost of coronavirus testing for some policyholders, but not the treatment. And saying a test or treatment is covered doesn't mean it's free.

The White House quickly clarified the President's remarks, saying Trump meant to echo Vice President Mike Pence, who said Tuesday that insurers had agreed to waive all co-pays on coronavirus testing and extend coverage for treatment.

Here's the deal:

Over the past week, many US insurers have said they will waive cost-sharing for coronavirus testing for certain policyholders. But that typically applies to the test, not to treatment -- and not even to the office visit in many cases.

What type of coverage you have matters. Many insurers have said that members in their individual market, Medicare Advantage and certain employer plans won't be subject to co-pays for testing, according to a list compiled by America's Health Insurance Plans, an industry group.

However, the majority of American workers are covered by large-employer policies in which the companies pay the claims. Many of these employees may still be on the hook for co-pays for the test unless their employers decide to waive the cost.

Certain insurers, including CVS' Aetna, Highmark and Humana, said that employers would have to opt-out of the cost-sharing waiver. Other carriers said they are working with companies to confirm their coverage.

Traditional Medicare, meanwhile, will cover the test. There is typically no cost sharing on clinical diagnostic laboratory tests, according to the Centers for Medicare and Medicaid Services. Medicaid benefits vary by state, but recipients typically pay little or nothing out of pocket for testing and services.

However, the coronavirus test is not the only charge patients may face. They might be responsible for the office visit and may have other tests done -- to make sure they don't have the flu, for instance.

How much they pay for these services depends on their annual deductible -- which is $1,655 on average for an individual -- and their co-pays.

United Healthcare, for instance, specifies in an FAQ on its website that it will handle the coronavirus office visit in the same way it does other provider visits based on one's health benefits plan. But Blue Cross Blue Shield of Massachusetts says it will waive co-pays for coronavirus treatment at doctor's offices, emergency rooms and urgent care centers.

Generally, going to an emergency room will be much more expensive than going to a doctor's office or urgent care center or using telehealth. Those not feeling well are advised to call their doctor before seeking care.

There is no specific treatment for coronavirus so doctors and hospitals will provide care for the symptoms, as they would for any infectious disease -- which is typically covered by insurance, said Kristine Grow, spokeswoman for the insurers' industry group. That means it is part of patients' insurance benefits packages, but likely still subject to deductibles and out-of-pocket costs.

Those who are seriously ill may be hospitalized, which could rack up big bills depending on treatment and insurance benefits. Grow suggests patients check their insurance plans to learn about the costs that may be involved.

After meeting with top executives from insurers and their industry groups Tuesday, Pence said the companies agreed to cover treatment. Were treatment not covered the charges could be far higher, and patients might be responsible for the full tab.

The issue of surprise billing -- which has been one of Trump's health care priorities -- is another matter. Surprise bills are typically generated when patients see out-of-network providers, often in emergency situations. People then usually receive large, unexpected bills from doctors and hospitals that their insurers decline to cover.

Trump has urged Congress to address surprise billing, one of American's biggest health care headaches. However, legislation has gotten bogged down amid infighting between insurers and providers, with each wanting the other to take responsibility for the majority of the charges.

The cost of coronavirus testing became more of an issue last week when the test kits started becoming available in commercial and hospital labs. Prior to that, the Centers for Disease Control and Prevention was picking up the tab for testing in public health labs.