At one time class A was anything up to .19. From there to .29 was "B", I think thru .40 was "C" and above that "D".
When the .049's (and others near that) came out, they established a class for smaller engines with a limit of .05 (in the USA), and named it 1/2A (even though it was only 1/4A in actuality). There is no OFFICIAL 1/4A and 1/8A as far as I know...it's just a size reference.
Later as more US flyers wanted to compete in FAI FF, the .19 size class "A" fell to the wayside popularity wise in favor of the .15. (FFers can correct me on this.)
There were several engine sizes on the class border. For 1/2A it was .049 and .051. For class A it was .19 and .201, etc.
The purpose was to allow a FF plane to fly in two classes without having to re-trim.
This is all from memory so please keep me honest.
George