Basically, there are derailers designed for big cogs versus derailers designed for small cogs and derailers designed for triples versus derailers designed for doubles/singles. The cage length, as others have mentioned, is designed to offer more wrap capacity; this is the numerical difference between the smallest/largest sprockets as well as the smallest/largest cogs. (Other strategies have been used as well;
feast your eyes!:
http://www.disraeligears.co.uk/Site/...system%29.html. Max cog is determined by geometric differences on the cage that go beyond my understanding and the scope of this thread, but consider that SRAM offers, for example, x9 rear derailers in short-, mid-, and long-cage versions, all of which have a max cog of 36t--but divergent chainwrap capacities.
It's also worth noting that both wrap and max cog is influenced by the length of the derailer hanger, too.
As a note, it seems that a lot of 'net bike mechanic "conventional wisdom" has been informed by Sheldon's site and the ubiquitous Shimano offerings that dominated the market at the dawn of the internet. When Sheldon wrote the bulk of his site, Shimano only made long-cage (sgs) r.derailers for mtb, and nothing longer than gs models for road groups. Which, in a way, made Sheldon's accurate crib sheets confusing to some, who got the correct info, but didn't understand the math/mechanics behind it all.
OP: read up a minute, then mess with the b-screw. Therein lies your fix. You may not
necessarily need a longer chain, but you ought to make sure you're running the correct length regardless before proceeding.