Absolutely, and it's an excellent question, honestly.
Most of the time as designers (print, web, UI/UX, etc.) we are used to seeing the model of "work for hire," which is where we just sell our services as a one-off, and then the client owns all of the work that you've done and the copyrights to it as well.
This is the most common scenario with traditional employment, but is definitely not the only way that it can go down.
For a full breakdown of pricing models, I would definitely recommend the AIGA's article on it here: