BFB seems to be the professional mecha-basketball sport, where as Basquash is a 'street' version of the game.
Basquash is the unofficial name for Big Foot Streetball and comes from 'baka' and 'sukasu', explained below
Ref
Big Foot Basketball (BFB)
A popular professional sports league on Earthdash. As its name suggests, it involves playing basketball with Big Foots. Its popularity dwindled however when Dunk Mask hijacked a game, resulting in the destruction of the Rollingtown stadium.
Basquash & Open City Basketball (OCB)
Open City Basketball, unofficially named Basquash by Dan and known earlier in the series as Big Foot Streetball. It is a new sport that involves playing streetball in a wide cityscape using Big Foots.
Prior to becoming an official sports league, Big Foot Streetball was outlawed due to the destruction it caused. Many of Dunk Mask's ardent fans prefer the name "Basquash" over the official name of the sport. Basquash is actually not the combination of the terms basketball and squash, but rather a pun in Japanese from the terms "baka" meaning "idiotic" and "sukasu" meaning "unintentional acts".
Dan uses the phrase against the The Worst leader, then in a flash of brilliance while chanting "baka" and "suka", starts saying "bakasuka". "bakasuka" is a word that means many, tons, or barrage of.
Basically Dan is jumping from word to word, punning his way, until he screams "Basquash" when he does the final squash serve-like attack, Basquash.
So, the sports are very similar, they're just slightly different.