What are the differences between these two receptacles?
The outlet on the left will accept both 15 amp  and 20 and compatible

The outlet on the right is a 15 amp only outlet

The left is formally a: NEMA R5-20R

The right is formally a: NEMA R5-15R

The designation is for the pin pattern alone

The shape of the 'Square' vs. the 'Double D' outline is cosmetic only

The square shape is typically called 'Decora' - the word Decora is a trademark of Leviton. But it is used generically.

At this point, I think you can actually get more things in the Decora pattern footprint. GFI, Motion sensors, and other devices come in the Docra pattern, but are not seen often, if at all in the double d format.



Both of the devices you show are in a 'Single Gang' and 'Duplex' format.

'Gang' is a trade unit of measure (2.812" x 1.75") and 'Duplex' refers to the fact that there are two of them.

The 'NEMA' (knee-ma) is the acronym for National Electrical Manufactures Association. Lots of information, but being a standard, it lacks the symmetrical debates that occur with the NEC

http://www.nema.org