Motion control shoes are for extreme overpronators. Neutral shoes have a uniform color and uniform density throughout the midsole. Neutral shoes are for neutral runners and udnerpronators. Underpronators and supinators need shoes that encourage pronation. Don't let this confuse you.
All shoes have a cushioning system.
Okay, you should be armed with enough knowledge to know what kind of shoe you're looking for. For those interested in more details, I will now throw in some further bits of information for your studying enjoyment. Every manufacturer has its own patented cushioning technology. Asics uses Gel, a pliable gel-like substance. Adidas uses Adiprene, similar in structure to the Sorbothane insoles you might find in a shoe store.