Does "another" mean "another" in mathematics?

I sometimes hear people saying something like

Let $f$ be a function from a set $A$ into another set $B$.

But, of course, by saying this, they do not want to exclude the possibility of $A$ and $B$ being equal, they just mean that $B$ can be different than $A$.

My question is: Is it, technically speaking, correct to use the word "another" in this case? Also, independent of the question whether "another" is correct or not, I wonder if the word "another" could confuse readers oder listeners, that is, if the word "another" is good from an expository point of view.

This is common usage but it really isn't a good thing. If one means that the set is distinct just say a "distinct set B." If B is possibly A then just say "from A to B" without any further comment. To some extent "another" in this context is a verbal "filler" that doesn't do much.

For that matter, it seems unlikely that there are going to be many contexts where one has a function from A to B and it is going to matter that A is not B while at the same time there won't be other stronger properties in use like A and B differing in cardinality or topology or metric.