Atomic is all-or-nothing upgrades / block upgrades instead of individual packages
Immutable is a read-only operating system root (yes, you have access to /etc, fedora got pedantic about this)
You can have one, the other, or both, or none.
See my reply to OP for sources but there are more than just the two I referenced.


No it’s not. Fedora got pedantic about the term “immutable” but there are more than a few that use Atomic or Immutable and they are different things.
Atomic is all-or-nothing upgrades, Immutable is a read-only OS structure (this is what Fedora got picky about as being ambiguous).