Just building off of what madave said: X-Men #1-66 were original stories, which are collected in two “The X-Men” omnis. Issues 67-93 (from approximately 1970-1975) were reprints of earlier stories. The X-Men continued to make guest appearances in other Marvel titles during this time — some of those guest appearances have been collected in omnis, some not, but many of us hope there will eventually be an “X-Men: The Lost Years” [or some similar title] omnibus collecting all of those guest appearances. (Nearly all of the guest appearances are collected in the Marvel Masterworks “The X-Men” volumes 7 and 8… if memory serves, it’s only missing a 2-page cameo Cyclops and Professor X made in Morbius’s solo feature in
Adventures into Fear.)
Then there was a ‘90s ongoing series called “X-Men: The Hidden Years” by John Byrne that attempted to tell stories of what the team was doing during the “reprint years” — that’s getting an omnibus later this year.
As for X-Men Classic, that’s something different. That title reprinted X-Men issues starting with Giant-Size X-Men #1 (the debut of the All-New, All-Different team in 1975), but with new pages and new stories added — sometimes to make subplots fit better with later stories, oftentimes to just flesh out characters more. The X-Men Classic omnibus doesn’t collect the original issues (which can be found in the Uncanny X-Men omnis, volumes 1 and 2), but it collects all of the extra material that was added in the X-Men Classic reprints. It’s heavy on solo character exploration stories, some of them quite good; but it’s definitely a companion to UXM omnibus volumes 1 and 2, not a replacement for them.
Hope that helps!