No, they aren't. I feel like I'm taking crazy pills reading these comments.

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.

https://ubuntu.com/blog/ubuntu-core-an-immutable-linux-desktop

https://fedoraproject.org/atomic-desktops/silverblue/

What is an immutable operating system? Before we can discuss what differentiates Ubuntu Core from other immutable operating systems, we must first define the properties that make an OS immutable:

Read-only: The primary characteristic of an immutable OS is that the running system cannot be directly modified by users or applications.

Atomic updates: Updates are applied atomically; meaning they’re successfully applied all at once or not at all.

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Edited for formatting.