Arguably, they're still closer to each other conceptually than to a "festival", "convention" or "masterclass" (for types we already have), or "rehearsal", "music camp", "radio show" (for examples of what's been requested).
"Stage performance" as a parent of "concert" sounds like it could possibly work? (a la "all concerts are stage performances but not all stage performances are concerts"). Sure, some concerts are not on a physical stage, but still. I'm not fully sure if that's still different enough from the other types, but I think it might be.