It’s pretty common for touring drummers to have multiple snares. Drummers usually switch between the drums, choosing the one whose tone best fits into the overall texture of each song. It’s uncommon for a drummer to use two snares over the course of a single song. Part of the difference in tone comes from the natural sound of the snare, which can vary quite a bit depending on the depth of the drum and the materials used for the drum heads and drum shell. The snare heads can also be tuned to different pitches, which affects not just the tone of the drum but also the way it responds.
At Radiohead shows, you can usually find multiple snares on stage. Phil has brought a pair of snare drums for Radiohead touring since ~1999, more info on his page. Phil also added triggers to both snare drums, allowing him to trigger sampled snare sounds on songs like I Might Be Wrong. And for Radiohead’s 2011-2012 and 2016-2018 tours, Clive Deamer brought three snares, each with a shell made of a different material!
A photo from Clive’s website, showing his setup for Radiohead’s 2016 tour. The snare closest to the camera is a Premier Signia Maple with a maple shell and maple rim. The one next to it is a Gretsch COB 5.5 with a brass shell (covered in chrome). The third snare, currently on the stand by the kit, is an Ludwig LM402 Acrolite with an aluminum body. See the post on Clive’s site for info on the drum heads.
A photo from Tom Skinner’s Instagram of his drum setup on stage for The Smile’s show in Lyon on June 8, 2022. It’s hard to identify his snare drums, but one has a noticeably deeper shell, which can lend a deeper sound. On a synthier note, the case on the right is custom-built to house the Elektron Octatrack MKI and Tiptop Audio Mantis eurorack case. The keyboard synth is Radiohead’s old Prophet ‘08.