Hazy IPAs (aka New England IPA) - Less bitter, more aromatic, fruitier compared to standard IPAs.
West Coast IPA - Hoppier (read: more bitter) than an IPA. Some say flavors of pine, resin, grapefruit, malt sweetness can be present.
The terms double and imperial are used throughout the brewing industry = stronger/higher ABV.
Imperial is generally reserved for stouts and porters, while double is claimed by everything else.
Certain terms, just like in herfing and piping, are occasionally used redundantly or all out incorrectly, e.g. the other day I saw a 5.5x50 cigar marked as a corona.
If you want to get deeper into the weeds read this:
The Nine Major Types of IPAs