While Stamos is a talented musician and singer, he did not perform all the songs attributed to Jesse. Some songs were recorded by professional singers, with Stamos's voice either dubbed over or mixed with other singers' vocals.
This is a common practice in television and film to ensure the best quality and professional sound for the songs used.
However, Stamos did contribute his own singing voice to some songs, including the iconic "Forever" which he co-wrote and performed with the Beach Boys.