Most bands have different live arrangements and improvise a lot live. Can you imagine playing the same song the same way for years on end? Also, studio tricks and instrumentation are not as readily available (although more available now if you have the money) live. When you see a live recording, it is probably the best take of a whole tour of performances, and doctored up in the studio afterward. Singers may not have the same range live as under ideal studio conditions. It may have taken 20 tries for the guitarist to get that riff perfect on the recording or the singer to hit that note. It may have even been accidental. As far as remembering stuff. Well..... some can, some can't. I'm an excellent backing vocalist but I could never remember all the lyrics to a long list of complex songs. Even ones I write. It's a gift front men and actors have. And they still screw up all of the time. And then there's telepromters nowadays on stage, canned vocals, pitch tracking, harmonizers, etc. Btw. A personal recorder and a notebook helps a lot.
Stage Guitars: '80s Thin line LP Custom, '70 LP Standard, '83 Squier Black Headstock Strat w/ Dan Torres pickups, '59 Black Danelectro DC, sometimes others.
Pedal Board: Nady UHF 10 -> TU2 -> Rocktron Big Crush -> 70s MXR Phase 100 -> Cry Baby -> Bad Monkey -> Early '80s Rat -> Early '80s Ibanez CS 9 -> Ibanez DE 7 -> Behringer Dr 100 Stereo Reverb
Stage amps: '63 Blonde Tremolux w/ two original 2X10 cabinets with a '60 Ampeg Rocket/18 watt VTB Marshall clone/ Epi VJ into a Mashall 1965A