A squash is the edible fruit of squash plant, but it's considered a vegetable in the kitchen, like peppers and tomatoes. As a verb, squash means to compress or mash — like the way your picky little sister might squash the roasted squash on her plate with a fork.
Squash that grows on a vine comes from the Native American Narragansett word askutasquash, "the things that can be eaten raw." The game called squash has nothing to do with this plant or its delicious fruit. This racket sport's name comes from the fact that players hit the soft rubber ball so hard that they squash it.