Most people get medical insurance through their employers. Each state makes its own rules and regulations concerning what plans and benefits are available to taxpaying residents of the state. Typically when you get a policy issued, it is on the person instead of the place. In other words, the policy goes wherever the person goes. If you travel to another state and get injured, you typically have coverage.
International travel is a different situation. Most policies will not provide any coverage outside of the United States or Canada or US territories. Medicare definitely does not cover international claims. Many retirees like to travel the world but should make sure they have adequate protection when traveling overseas. Fortunately there are very affordable plans available that cover international medical insurance claims specifically. These plans cover more than just medical expenses. Typically they can also cover things such as lost luggage, emergency evacuation, repatriation of remains, and acts of terrorism. But the most important expense most people should be concerned with is the payment of medical bills if you are hospitalized outside of your home country. Make sure you have adequate protection.
One exception to the general rule that your coverage goes with you wherever you go in the United States would be with HMO types of plans. These HMO plans keep costs low by partnering with doctors and hospitals for special deals. If you go to those doctors and facilities, you will get a great deal on services. Sometimes if you go to a doctor who is not in the network, you may not have any coverage at all. So the problem you may find if you travel to another state is that there are no network doctors in your area. While you would likely be covered for emergencies, that is probably the extent of your coverage.
People generally change policies when they are in transition. Sometimes if you move from one state to another you need to get a new insurance plan. Short term health insurance plans are great for these situations. Once you get the coverage, you are covered the same no matter where you go. Students who go out of state to college or graduate and get a job in another state often get short term health insurance plans to save money and give them coverage. This insurance will cover them no matter what state they might get a job in. Even if you move to a state that does not allow these types of plans. If you get injured or sick, you will be covered if you have the plan on yourself.