Regular Cabs are defined as 2-door cabs, with a single row of seats. There is little or no space behind the seat. An "extended cab" has a set of rear doors which are rear-hinged, that is, the hinges are opposite the front door hinges. (This door style is sometimes called 'suicide doors'.)
The term "double cab" is the industry phrase to define a 4-door pickup cab with 4 conventionally-hinged (front hinged) doors, but with the rear doors noticeably shorter than the front doors.
Aptly named as it's the body style which most easily carries "the crew", a crew cab has 4 full-size forward-hinged doors (front and rear doors about the same size) and a full rear seat. Be careful, as at a quick glance a crew cab can easily be mistaken for a double cab, or vice versa.
Unique to Ram, and found only in their heavy-duty (2500 and 3500) series, the "Mega Cab" is a crew cab plus a little more. While the 4 forward doors are similar to a crew cab, the cab itself is stretched behind the rear seat, providing additional inside storage room.