Is it weird that 'pick and roll' basketball is called 'double-teaming'?

catefrances

EvilMerlin wrote:

However if you choose to go to another player, or shoot yourself, and not go to the rolling player, then a pick and roll was never executed. As Jasonw was saying, that's not a pick and roll.

That's just another player setting a pick. You must pick, seal your defender, have an open lane for the pass and finish. Then you've had a pick and roll.

i disagree.
if the pick has been set and the defender makes contact, the screen pivots, and rolls toward the basket. this is the pick and roll play, no? if for some reason the defender chooses to stay on the screen and a clean pass cant be executed back to him, i dont see how that negates the pick and roll move.