@Chlidonias Interesting, I didn't know that. Were the true button quail ever actually considered Phasianidae? Or has the inclusion come about simply because of similarity?
@Great Argus They have been but you're going back a long way. The use of the name for the Painted Quail is not really anything to do with true buttonquails though, it simply signifies "small quail" (e.g. in relation to Japanese Quail and other similar species).
There are lots of cases in the pet trade of one name being used for an unrelated species. A good example is that in the USA (in particular) budgies were typically called "lovebirds" during parts of the 20th century, and are still commonly simply called "parakeets" there (which is the shortened form of the even older name, "shell parakeet" [obviously budgies are a species of parakeet, but it still isn't a helpful name to use]).
@Chlidonias
This is quite true. I suppose "buttonquail" might be more of a relative term, like how people call bison "buffalo" although they are not the same thing.