Atomic in software refers to an operation that cant be interrupted because it happens in one step. This one of the big selling points of atomic or immutable distros. Your system will not be left in a broken state by cancelling an update because updates do not take multiple steps, unlike traditional distros.
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 people do configure snapshits before all updates.
Fedora has pushed for the change by rebranding their immutable distros as Fedora Atomic Desktops, and these are likely the most popular immutable distros. Bazzite's homepage also describes the distro as atomic, but never mentions the term immutable.
How is atomic less confusing? Immutable means that something doesn't change, atomic means that it's the size of an atom or has nuclear energy
EDIT: I've learned that some people are overly pedantic about the meaning and practical use of the word "immutable", so much so that they decided to create a bigger confusion by giving another word a completely different and exclusive meaning
Atomic in software refers to an operation that cannot be interrupted, like the updates in these distros. Immutable is a more confusing term, as it leads users to believe that cannot control parts of the system, when in reality these distros still have tools to do so.
Settings live in user space. Software exist in containers like AppImage, Flatpak or Distrobox. If something need deep system integration, they can be layered on top of the system in the user layer. Immutable does NOT mean less control. Just exerting control over the system in a different, usually more systematic, automatic and deterministic way.
The main difference to your examples is that an "immutable OS" is in fact mutable, while none of your examples describe themselves with an adjective that is contradicting with their function/inner workings.
Flatpak is a pretty good name, because it makes software flat in the sense that it avoids having a (tall) dependency tree.
Also bottles has no IT related meaning, while immutable does.
"Immutable OS" is not a product name.
An "immutable" OS becomes mutable whenever a user wants to change anything on it.
Now imagine I keep describing my car as undrivable, because it only becomes drivable when somebody gets in and drives it. - You'd think that this is a completely deranged statement.