The Chinese Blue Breasted Quail (aka button quail) that we know are not true button quail per se. They just got the nickname because of their size. Here is an excerpt from the most correct book on the market. A Closer Look at Button Quail by Jodi McDonald
"The nickname "Button Quail" soon caught on and spread throughout the world, but there was a problem. There is a true species of birds with the nomenclature "Button Quail," that make up 15 species of the order Guriformes, family Turnicade and genius Turnix. True Button Quail are native to many parts of the world including Africa, Asia, India, Sri Lanka and Australia. To further complicate the issue, True Button Quail, are not quail at all.
The little Chinese Blue Breasted Quail are easily distinguished from True Button Quail by looking at their toes. True Button Quail are hemipodes (Greek word meaning half foot.) They have only three toes, all of which point forward, they completely lack a hind toe, whereas Chinese Blue Breasted Quail have four toes, three that point forward and a hind toe that faces backward."
The hemipodes are found in some zoos. They are very hard to own in captivity. I know someone who had some (not anymore) who had a few and their eggs were never fertile. It is very difficult to raise. Some birds are not meant to have in captivity and should just stay in nature.