I'm not entirely sure I believe that isn't what "talking with each other" is. How are those two fundamentally different things?
Because when I talk in person with friends and family, it's mostly just us sharing our opinions and observations back and forth.
If we're asking what people mean when they use those descriptors, then you're correct.
However, literally speaking, in this context, immutable only means read-only, and atomic only means that updates are applied all-at-once or not at all (no weird in-between state if your update crashes halfway through).
The rest of the features (rollbacks, containerization, and immutable meaning full system image updates) are typically implied, but not explicitly part of the definition.