You have to distinguish between debit cards and credit cards. All cards are part of a specific payment network. There exist for example Visa/MasterCard, American Express and Discover, just to name a few. All of these cards are accepted everywhere where this specific payment network is accepted. For example if you see a visa logo you can pay at this location with your Visa card no matter which bank issued you the card.
The difference between prepaid/debit and credit cards is, that these cards have limits. For the first category it's the funds in your bank account/the amount you put on it and for the second, CC, it is a limit based on your income and creditworthiness. Normally this makes no difference. But if you would rent a car or book a hotel room they normally secure some amount on your card. For prepaid/debit cards you have to have the money to pay for your hotel room and the deposit. For a real credit card your limit just has to exceed the deposit and you're fine.
Keep also in mind, that you are not building credit history with a prepaid card.