I don't use it alot myself, however, you can send BTC to anyone having a BTC address, they don't have to be registered on the same 'bitcoin wallet'. I believe it's the most common one.
You shall wait for another reply due to me being inexperienced in this field, have a nice day.
BTC is one currency, such as dollars or sterling. Imagine wallets as banks. You can send money to another person by transferring it to their bank account, and this will work regardless of the bank that you're registered with. It's the same idea with BTC wallets, except the money in a BTC wallet is solely yours. In short, it doesn't matter which wallet you sign up with, as long as it is trusted and secure.