Musical works. Performance rights organizations (ASCAP, BMI and SESAC) handle copyright licenses for the performance of musical works, including their performance in a podcast. Separate licenses are necessary from each performance rights organization because each company represents different publishers of composers' musical works.
Sound recordings. Copyright licenses for the playing (or "performance") of sound recordings historically have been handled directly with the owners of the works, usually record companies. (Over-the-air broadcasters are not required to obtain copyright licenses for playing sound recordings. They must, however, hold licenses for playing the underlying musical works.)