You're over thinking it.
Also, I see a thread exactly like this posted every few weeks, and it never goes well.
Parenting isn't black and white all the time.
Just because someone says they are a "full time mum", it doesn't mean, by extension, they are calling you a part time mum.
Likewise, if someone says they are an "attachment parent", it doesn't mean, by extension, they are clung you a non-attachment parent.
I could go on.
So, when parents describe something about themselves, they tend not to be thinking about other parents or how they should be labelled.
What should full time mums / SAHMs call themselves, OP? "I'm-a-full-time-mum-but-of-course-I'm-not-saying-you're-a-part-time-mum" is a bit wordy.