When a made the puzzle on the left in July 2009 I used the name Stretchex since I stretched out the top and bottom of the puzzle. I believe they look the same.
Indeed. They are the same. Sorry.
But that solves the naming problem.
How many 3x3x3 mods have you made all together?
I have taken this from my personal "done it"-tree:
36 Sticker variations
54 bandaged 3x3x3
18 straight extended 3x3x3's
17 other 3x3x3 with glued on cubies
33 3x3x3's truncated like octagon's edges
4 truncated with sharp corners
21 with regular truncated corners
18 other truncated variants
10 Siamese and Triamese 3x3x3's
9 wacky bandaged puzzle (most consisting of more than one 3x3x3)
7 StandardPieces 3x3x3's
8 variants with Fisher-Edges
16 variants truncated like the octagonal edges and afterwards extended
12 sharp edges extended variants
5 different sized traijbers octahedra
7 with regular truncated corners and afterwards extended
10 other strangely extended cubes
3 variants difficult to classify
292 variants but one dozen or so are not made by me.
It's a textual encoding of the geometry of the puzzle.
Perfectly true. I want to mention that the encoding method somewhat change with the category. So SharpCorners8800101000 is something different than SharpEdges8800101000.