I would say Calvinism says there is a choice, but I would disagree with their definition of choice fundamentally.
The calvinist's perspective is that man's will is corrupt to where he will always choose evil, so he does what he wants to do, although he really can't do anything else.
It is soft determinism. The will is set as well as the actions so the being always chooses what they want, but what they want is preset as well.
Arm
Enianism is a nationality. The same nationality as the dudes in system of a down.

(It is a common, but amusing typo, especially since in real life my name gets me tagged as Armenian even though I am not, and am whiter than sour cream)
Arminianism holds the view that man can pretty much only choose evil by nature as well, because we are evil. It is the result of fall and not divine decree. Still, very much bound. The differences are actually pretty subtle.