A session musician is a musician who records with you but is not officially part of your band. Session musicians are paid a flat rate for their services rather than receiving a royalty, but they do receive credit in your liner notes.
Some session musicians work tied to a particular studio and work on recording sessions there, while others work freelance and go from studio to studio as requested by the musicians who are hiring them. Still other session musicians do a combination of the two.
Although the studio is really the home of the session musician, some do tour with bands and perform in the live shows as well.
Pay for session musicians varies from project to project and country to country.