First of all I think you actually want the distance from the regex to a fixed string, not between two regex. This is possibly a (slightly) easier problem.
Secondly I suspect that the problem (at least for regex but maybe not for glob) is undecidable. Consider the matchs:
/(ab|ac|ce).{3}(ge|ef|gh)/
aceabdef
ageabdxf
Clearly the regex matches the first string (i.e a distance of 0), but for the second you could validly be asking "How many modifications to the regex are required to create a match" or "How many inserts/deletes are needed on the string for the regex to match". These are of course different questions.
If you think of the pattern space of all possible strings then each string is a single location while a regex is an area. It is quite legitimate to ask for the distance between two points, and that is easy to calculate. It is also possible to ask if a region encloses a point, that is does a string match a regex. The question you are asking is what is the distance from the nearest point in an area. Simple changes in the regex can have large effects on the area covered. The power of regex makes your question hard.