If you've got to use a family term to refer to me, I prefer Aunt/Auntie/Aunty to Mom/etc. and/or Grandma/etc. Like, I'll shut you down hard if you try to call me Momma Dee, not because I don't want to feel connected to you, but because of the following.
First, Aunt can be used to refer to just about any age-range, so you lose the implication that whoever you're referring to is so old that they can't comprehend or emphasize with anything you might want to come to them about. I'm hardly sensitive about my age (I'll admit to anyone who asks that I'm 39), but I know that a lot of younger folks automatically ignore anything they hear coming from someone they deem "too old to possibly understand".
Second, while all three terms imply a family bond, Aunt has less of a connection, and less of a sense of obligation on both sides. Not saying you don't worry about disappointing your aunt if you do something wrong, but it's no where near the sort of guilt folks usually experience when disappointing their mother or grandmother. Again, this makes it easier to have frank discussions where I can give advice without anyone feeling terribly awful about it.
Third, I'm a real stickler about responsibility. Moms (and often Grandmoms, in this day & age) should provide almost everything for their children. (I know this doesn't always happen, but that's not what this is about.) While I'm happy to help folks when I can, I'm by no means capable of doing everything, and I certainly don't want to be associated with the expectation of being able to do so. Aunts, on the other hand, are there as often as they can be, but there's no judgement if they miss something.
Fourth, Aunts don't have to be a perfect role model. If I want to buy my nephew 100 chicken nuggets for his birthday, or an entire adult-sized burger entree with a monster milkshake, well that's something I can do because I'm his aunt, and it's a special occasion. If I want to shower my adopted social media family with gifts and hilarious anecdotes, sure, go for it. That's just what aunts do. But if I can't? Well, I have no responsibility to do it in the first place.
And finally, a very personal reason. I have no desire to have children of my own, and that desire ripples out to include even internet kids. I have nothing against kids (as anyone who knows my interactions with the Niblings will attest to), I just. Really don't want the responsibility that comes with caring for them, as I can barely care for myself some days. Being a parent is a 24/7 job, with no vacations, and I just. Can't. Fathom.
I know a lot of these are just my personal interpretations, but since they are things I associate with the word Mom, I'd rather not be called it. But everyone out there is free to call me Aunt.