"Invulnerable" != "Immune to CC". It just reduces all damage you'd take to 0 (similar to Trynd while ulting and at 1HP). Even "immune to CC" doesn't necessarily remove CC unless the ability explicitly says that. As an example, Vi can get stunned or snared mid-ult, and the CC effect will happen when the ult ends of the CC hasn't worn off yet.
"Untargetable" = cannot have any NEW abilities applied to you, and you can't be damaged by most targeted or AOE abilities. Going untargetable (e.g. Fizz pole / Vlad pool) does not remove debuffs, tethers, or ongoing DOT effects, so you'll still take damage from those.
Zhonya's makes you untargetable+invulnerable, but does not remove CC/debuffs/tethers/DOTs. They won't damage you while you're in stasis, but they can pick back up afterwards if they're still in effect.