OK, lemme try !
Mini Hums were made, because, at the time, there were only P90 pick ups (on the Gibson side of things)
Then, when the full size Humbucker came out, everyone wanted one, and all of a sudden, Gibson had all these P90 routed bodies that might not sell.
So, the clever folks at Gibson, made a 'smaller' version of the Humbucker, (and named it the Mini-Humbucker), so that this new version can slot into the P90 cavity.
So, that it the reason why the Mini Humbucker exists.
In a very crude nut shell :
A P90 sounds 'kinda' between a single coil (strat) and a full size Humbucker. (...to my ears)
A Mini Humbucker sounds much more like a full size Humbucker, but ever so much '
thinner'. (just listen to Johnny Winter)