There are three main types, and a couple of variations of each. Most use a 5/8" axle, but newer ones tend toward 15mm.
Early trikes mounted both rear wheels in "fork" structures, and used a jack shaft to transfer power from the right-side chain line of the bike to a short chain on the inside of the left wheel. These used standard bicycle wheels - two fronts and one rear, usually coaster brake - and are normally found on light duty "adult" trikes from last century.
The more modern, medium duty trikes use a live axle arrangement in the rear (5/8" or 15mm) and drive one of the rear hollow-hub wheels either via a keyed hub or through a bolt-on arrangement. The axle may be driven directly from the main bike chain via an axle-mounted freewheel (necessitating a band, drum or disc to be mounted on the axle), or by using a bicycle hub as a jackshaft in between, in which case it is usually a 1 or 3 speed coaster hub with an extra cog mounted to the hub body to drive the axle via a short chain.
I think the units with the extra hub in the rear and the 15mm axles are likely strongest of the bolt-on options.