Wide and broad can mean the same thing, but generally we say "broad shoulders" and "wide roads" as common collocations. There are other preferred usages but they are not written down anywhere to my knowledge. Just learn them as you go. Wide skies but broad horizons; wide-eyed but broadband; wide berth but broad beams on a ship.

I prefer "broad shoulders" but in fact, I have seen "wide" and "broad" used synonymously for shoulders, range, area and other nouns. There is no difference in meaning but it's possible that one or the other are preferable in certain collocations. "to have broad shoulders" also has a figurative meaning to describe someone who has a great capacity to accept responsibility and/or criticism.

Shoulders are broad. You use wide when referring to a space between objects or the player shoots wide of the goal.