If you have private insurance (which is usually offered if you hold a full-time job through your employer), you will most likely be paying a certain amount every month for it. Then when you go to the doctor or hospital you may have a copay or deductible to meet and then the insurance pays. Sometimes they don't cover everything and you get a bill for what the insurance company doesn't pay.
This is totally different from government funded programs if you can't afford it. They pay everything but it could be a challenge qualifying for these.
Most, if not all, hospitals have a certain amount of money that they give away per year for those that can't afford services. You you don't have insurance and you have an emergency you can go to the hospital and the bill will be sent to you. You can try applying for this program then (after you generate a bill in some or all hospitals). It doesn't mean you'll get accepted though.
If you go to the doctor with no insurance you pay the bill.
It's hard to say whether this is the same across the US though.
I hope I explained that right.
