Yes indeed the chains are different.
Long time ago before global warming and the political climit of today,these small saws ran 1/4" chain,basically the same type used on carving saws.You could get this small chain in varies type cutters,chipper,round chisel and believe it or not round chisel skip.
Along came wizards such as Ralph Nader to protect mankind from itself and through the process of the "squeeky hinge gets the oil ",caused these type chains to be taken off the market.This along with Corvairs,convertable tops on autos and a whole host of other things,thanks again Mr. Nader.
I suppose depending on the saw as to what is available,these small saws could possibley be changed to 1/4" .As I understand it,chisel is available in the form of carving chain.The stuff is rather pricey per drive length plus at that size it takes quite a few to make a chain loop.Other than a tiny little toy "hotsaw" I don't see the point .