Given names often turned into family names when people were identified by their father's name. For example, the first name Ahrend developed into the family name Ahrends by adding a genitive s-ending, as in Ahrend's son. Examples: Ahrends, Burkhard, Wulff, Friedrich, Benz.
So accordingly. 1  some crouching positions are squats. 2  some crouching positions may not be squats. 3  squatting is not implicity crouching.  squatting and crouching are terms with different but overlapping definitions, the former more specific to posture, the latter to 1  motivation. squat is not a synonym for crouch.
Yes, but squatting shoulder width will train more muscle mass, and sumo squatting will train the muscles which 'operate' (to simplify it) at the wide stance, which incidentally is the stance which someone is likely able to squat the most*, due to leverages and range of motion.