A recorder is a flute, more specifically, a fipple flute. But there are other fipple flutes, such as tin whistles. (One distinguishing feature of a recorder i

A recorder is a flute, more specifically, a fipple flute. But there are other fipple flutes, such as tin whistles. (One distinguishing feature of a recorder is the use of the thumb hole to control octaves.) So calling a recorder a "flute" isn't exactly wrong, but is under-specific. Also, nowadays transverse flutes are often called just "flutes", inviting confusion if you call a recorder a flute. The etymology you reference seems speculative, not really contradicting the article's claim that the etymology isn't clear.