Flexibility and mobility are two terms often used interchangeably. People stretch and call it mobilizing, or say they need to “get loose” before a workout. I say the same things from time to time out of habit, but they’re not entirely accurate nor is “getting loose” before a workout as beneficial as you may think.
Having limited range of motion in your shoulders makes a variety of movements quite difficult; even painful. Overhead squats, snatches, jerks, pull-ups, muscles ups, and more all involve healthy shoulder mobility. If you've ever tried to perform an overhead squat with tight shoulders, you know what I'm talking about.