Pretzel chairs with different armrest, are these designed by Cherner?  

Variously...
Variously Cherner/Goldman/"Bernardo", Cherner seems to have "won" because that's the name the "real" chairs are made under today. I have one with the "Bernardo" label.
The chair is best with the narrow waist, originally about 2". These chairs changed as Plycraft tried to cut costs.
The later Plycraft chairs got kind of crappy and you can tell readily by the waist and the finish, sometimes they're kind of hideous, one was in the TV show House and I think either Dexter or his sister has one too.

Not a true Cherner design
As noted, Plycraft altered the design over the years. The altered versions don't look good, in my opinion.