Would it be possible to separate the two. I have read manga with this tag and some of them have "rushed" endings but some just... stop. The former I don't mind too much, the latter I really don't like.

After reading 142 manga with the "Rushed Ending / Axed" tag, some of which felt more complete than actually finished manga, I get the feeling the tag is in need of refinement.
For now, a "Rushed Ending / Axed" tag is NOT the same as no ending(axed). Or have I just misunderstood the meaning of Axed? I shouldn't have to read the manga to find out which of the two that was the right one.

Therefore I think that the tag needs to be modified. Or maybe add a new tag for manga that really doesn't have an ending... (Or does that tag already exist?)

~4400 manga completed
~1700 ongoing...

I've always found that tag odd as it means one or the other and not both. It's frankly just guesswork with that tag.
I think it should be divided into "Rushed Ending" and "Axed/Discontinued" or just "Discontinued". That way it'd be easier to filter out discontinued works (Flower Flower and Prism (HIGASHIYAMA Shou) comes to mind in this case) when searching as right now you'll only find that information under "Status in Country of Origin" section on each series' page.

The thing that's annoying about this is that mangaka almost always receive notice of their manga being axed so it's not like it blindsides them. T_T Mx0

Currently Reading: Gave up counting after 100 Manga...
Currently Watching: everything

Rushed/axed essentially means canceled and why there is a separate tag for that is beyond me. People haven't optimized the whole tag system yet so there is overlap in taggs sometimes. In general less specific tags are better to group things than very specific terms.