My experience is that there's absolutely no canonical answer to your question--different shoes manufacturers do different things with their "cushion," "stability," etc and once you're somewhat out of the normal minor corrective issues, you're on your own.
I had plantar fascitis, go custom orthotics, switched to adidas control shoes for 2 years, though only arrived at them after several months of trying different shoes. Then I developed IT band issues (very common with orthotics), new adidas control shoes (I was told by a sports podiatrist that the adidas shoe designer focused on forefoot control more than others) that worked, blah blah. All in consultation with a PT that watched my stride as I tried different shoes on a tread mill (Rebecca Kern Steiner, New Dimensions Physical Therapy, Austin, TX, could not recommend her more. a true life saver).
4 yrs later, new orthotics. Adidas stops making shoes that work for me, and after running in 15 different pairs (no lie) I surprise myself by getting Reebok DMX Stability, which after some IT band pain and breakin, work great. I buy 4 pairs.
To pick the right shoes out, I recommend RoadRunnerSports.com. If you pay the 25 to be a member, you get to try the shoes for 2 months and get a full refund. So while with those 15 pairs I racked up a lot of postal fees and heartache, I found the right pair. And RRS were so nice about--I got chirpy emails about "better luck next time" when I'd send one set of failures back.
If you have a good run store, that's an option (NYC is surprising weak is this regard), but sometimes even the best stores have a) inexpert advice (yeah, runners work there, but not runners that have experienced my pain), and b) draconian return policies and not even a tread mill in the store (this could be an insurance issue). After being saddled with one unreturnable pair of shoes, I switched to RRS, more than worth the postal hassle.