Hot Soda Apparatus - Lacrosse lyrics

The other day, I saw a few guys playing lacrosse in a field between two buildings. When I saw them, my attention was immediately drawn first to the ball they were tossing about, and then to those weird sticks in their hands. My subconscious then told my conscious mind, "Hey, they're playing lacrosse!"

From that point, I began wondering. Where did they come up with a word like 'lacrosse' to describe that? I remembered that it's also called field hockey, so presumably, the point of the game is similar to that of hockey. But then, as I pictured a hockey game, the similarites between hockey and soccer (or fútbol) came to mind. And soccer, too, is played on a field, is it not? So why don't they call that field hockey?

Lacrosse. Makes sense to me.