If I use my lawnmower to make ice cream, it will probably still be called a lawn mower. Guitar picks are used to pick the strings. A flat pick can also strum the strings, but it is the same flat pick doing a slightly different job. And strumming is just one way to "pick" the guitar. Although it may not seem like it, the English language does try to avoid some confusion; like the confusion of using two names for an object just because it has two functions. English usually sticks with the primary function.
When I was camping in the Boy Scouts, we did not call toilet paper toilet paper. We called it all purpose paper because it served so many purposes (may your imagination roam freely!)
Roger in Baltimore