Any question answered...

Depending on manufacturer and product class, long cage won't necessairly accommodate a larger maximum sprocket, but it will take up chain slack for a greater total difference. Total difference is [biggest sprocket - smallest sprocket]+[biggest chainring - smallest chainring]

It isn't (usually), and you go to a long cage when you need to accomodate a total difference greater than the capacity of a short cage mech. On road bikes, that usually means when you have a triple chainset, as most road groups will only accomodate a 16t difference in chainrings on a double and the corresponding short cage rear mech is designed to take that plus the difference between 11t and the largest sprocket permitted by the rear mech.

In the olden days, all MTBs had triple chainrings so all MTB rear mechs were long cage, but now that 2x10 and even 1x11 set ups are fashionable you can gain a bit of improved rear mech performance and lose some weight by using a mid or short cage rear mech if you don't need the full capacity of a long cage.

I understand now. Thanks.