Cou-de-pied and Coupé are two terms that I often hear used interchangeably by teachers, but there is a difference. The long and the short of it is that cou-de-pied is a position and coupé is an action.
Cou-de-pied - [kud(ә)pje] pronounced "cou" as in barracuda, "de" as if you were the sound that the letter D makes, "pied" sounding like p+yay (always trying to avoid that final y sound that is prominent in English).
Literally meaning neck of the foot, cou-de-pied is the part of the body located on the front of the body at the articulation of the leg and foot. The cou-de-pied would be under the spot where you tie your sneaker.
Depending on your preferred school of ballet, you may consider cou-de-pied to be a stretched foot position with the working toes touching near the ankle bone of the supporting foot. Today this position can be performed devant or derrière, wrapped or not wrapped. You might also consider cou-de-pied as a position in which the heel of the working foot touches near the ankle of the supporting foot and the working foot in a semi-flexed position so that the toes touch the ground. Many teachers call this position coupé. I won't say this is in error because it is incredibly widespread and is more of a linguistic evolution than a mistake, but some teachers find great value in making a distinction between the two. In either case, cou-de-pied designates a position of the foot rather than an action.
Coupé - [kupe] pronounced "cou" as in barracuda, "pé" sounding like the English word pay without the final y.
The verb couper means "to cut," and coupé was originally adjective describing the noun pas meaning "step," but with time and frequent usage, the word coupé became a noun in its own right.
One leg or one foot cuts under the body to replace the original standing foot. The foot that is replaced can be picked up in an extended position devant, derrière, or à la seconde or can be picked up in cou-de-pied or a number of other positions.
The frequent execution of coupé picking the replaced foot up into cou-de-pied may be one of the reasons that cou-de-pied is in many cases overshadowed by coupé.