I figured in the end that if people want to create/use 'generalized-functions', they are free to do so. My goal was only to sort out the mess that was 'distributions'. So I created 'schwartz-distributions' to try to prevent future confusions.

I will re-tag the distributions in the sense of analysis as schwartz-distributions.

It's true that anybody with sufficient rep can recreate a bad tag, but most people try to use popular existing tags whenever possible.

But at the very least I think distribution and distributions should be merged.

Secondly, however, I feel that those tags are bad, bad tags because distribution is such an overloaded word in mathematics. Under distributions we find questions about probability distributions as well as generalized functions. Under distribution we also find questions about geometrical distributions (in the sense of subsets of the tangent bundle of a manifold). This is likely to lead to much confusion.

Luckily, so far only 12 questions total are using those tags. Presumeably we can clean this up by hand with not too much trouble. But I am not sure how we should do this. One idea I have is to split into three tags probability-distributions, geometrical-distributions (I'm not so sure about the name of this one, a better suggestion?), and distributions-and-generalized-functions (which can be merged from the generalized-functions tag). Any comments?