I’ve gone through my copies of the liner notes that accompanied the two-fer CD re-releases of The Beach Boys catalogue in the early 90s. David Leaf compiled these using session notes, tape boxes, remaster engineer Mark Linnet interviews and union sheets to verify The Beach Boys played mostly live in the studio as a self-contained band from their debut through Shut Down Vol. 2, ie their first five LPs. There were an occasional piano or guitar as mentioned in OFFNY’s first reply, but it was for the most part The Beach Boys doing their own sessions for those records. I do see two drum tracks by Hal Blaine on Shut Down Vol. 2 and various other session players sprinkled in on assorted tracks because by that time Brian Wilson was starting to try to achieve and surpass the Phil Spector “Wall of Sound”. You’ll see tympani, a more accomplished pianist (Leon Russell) and various bells and percussion supplementing the basic five Beach Boys basic rhythm tracks. And around late ‘64, Brian decided to come off the road and start tracks without the band. So from ‘62, ‘63 and most of ‘64, it was the touring Beach Boys (the core band we all know as the early Beach Boys) on their own records with just assorted session guys spicing up the original basic tracks. On the first 3, it’s almost all them with hardly any supporting musicians at all. And just a few added pianos, percussion and Dennis stepping aside on drums for at most, 3 tracks on Surfer Girl and Shut Down Vol. 2. From there on out, Brian went full blast with his attempt to update and surpass Spector and the session guys emerged as his the core studio instruments through Summer Day’s / Summer Nights through Pet Sounds (and if counting the SMiLE sessions which went unreleased for over 40 years). By Smiley Smile, Wild Honey and the subsequent late 60s and early 70s, The Beach Boys were back to being the core band in the studio. Brian had stepped aside and Carl was the defacto live and studio band leader. And surprisingly, he learned well from Brian and those are some gorgeous records.
As for the Byrds, session players were only used for tracks 1 and 8 on their debut LP Mr. Tambourine Man. The rest were Clark, Clarke, McGuinn, Hillman and Crosby themselves. They continued to have *guest* session men on supporting instruments here and there, but the only Byrd who was subbed out from the 2nd LP onward was drummer Michael Clarke. Jim Gordon was a frequent session replacement for him when he could not get the sound the producer and McGuinn were seeking. By ‘67, he was gone and the drum chair was a revolving door until the Clarence White era of the band emerged in Hillman and Crosby’s departure.