Definitly a chasse, and for the record pirouette means to turn...so it's not a type of turn. just sayin'.
Fouette turns are done in one stationary position, and pique turns are usually done travelling. Also, in a fouette turn, the working leg does not ever touch the ground, whereas the working leg in a pique turn goes down to the floor between each turn. They are two completely different turns, but these are some basic differences. Also, fouettes are much more difficult, haha.
Pique means "to prick". There are different kinds. At the barre they are used, like little quick taps of the tip of the toe with a fully extended and pointed leg. The accent is up, much like pricking someone with a pin. It's not a stab, but a quick tap. In center they can be used differently. Pique turns, difficult to describe, but you push/slightly jump to an extended leg, to the ball of the foot or pointe, and turn. Also a pique can be a pique arabesque, same idea as the turn but it goes to an arabesque. I have taught ballet for 10 years and was a professional for 11. I have seen and done too many to count.
Pique
They pique her when she was changing her dress.
Gerrard Pique played for Manchester united.
Yes Gerrard Pique has a car it is a Mini cooper.
The Pique Poquette of Paris was created in 1966.
Pique Newsmagazine was created on 1994-11-25.
couverture de pique-nique
To have a picnic is "pique-niquer" (verb) in French.
The word "pique" has one syllable.