Here's a definition from Dictionary.com www.dictionary.com/browse/estrangement
estrange
[ ih-streynj ]
verb (used with object), es·tranged, es·trang·ing.
to turn away in feeling or affection; make unfriendly or hostile; alienate the affections of: Their quarrel estranged the two friends.
to remove to or keep at a distance: The necessity for traveling on business has estranged him from his family.
So yes, it seems to be that "estranged" or "estrangement," etc. could refer to a number of scenarios. Often, we use it here to refer to when someone goes totally NC. But it could also refer to a relationship that is very distant and strained. However, Hilda, unfortunately, many GPs are finding themselves pushed away or totally CO (cut off) from their AC, CIL, and GC. So I understand having some threads that talk about estrangement in general. We can tell what a poster's individual situation is via their reply if they give us enough details.
As for the OP, she did post one thread describing her specific situation, asking if she should try to reconcile w/ her estranged mum. And most posters told her that her mum doesn't seem capable of the kind of mother/daughter relationship she would like. So IDKY the general threads, unless she's just trying to measure her situation against others. If that's the case, I hope she realizes that what you're saying is true, that every case is different, and there's no guarantee that her mum's reaction would reflect those indicated here.
However, Purple, I'm sorry, but I think the "I'd rather not" posts come the closest, especially if you're hoping for a close relationship. And I agree w/MOnica that it would be best to seek counseling to help you come to terms. Please let us know what you decide.