I disagree, because they are not the same thing.
Immutable means read only root.
Atomic means that updates are done in a snapshotted manner somehow. It usually means that if an update fails, your system is not in a half working state, but instead will be reverted to the last working state, and that updates are all or nothing.
I create a btrfs snapshot before updates on my Arch Linux system. This is atomic, but not immutable.*
There is also “image based” which distros like ublue (immutable, atomic) are, but Nixos (also immutable and atomic) are not.
*only really before big updates tbh, but I know some people do configure snapshits before all updates.