Like if you watched the old Broly (the first one) He looked way younger, and in the DBS version he looks very old. So does that mean Goku, Vegeta, Gohan, Piccolo and Trunks minds where whipped clean?
Because of his limited appearances, fans have debated if Broly can be considered part of the larger Dragon Ball canon for years. But in a note on the Dragon Ball Super: Broly website, series creator Akira Toriyama said he worked to fit Broly into the Dragon Ball universe.
Hopefully that links confirms that Broly is canon now. The movie basically retcons Broly's origin. That's why his father looks older and different than in the DBZ Movie.
I think Toei wanted to distinguish between the canon and noncanon versions of Paragus so fans don't get confused when making fanart. As Gary said, you really shouldn't think of these two characters as existing in a uniform timeline and universe as one is canon and the other is noncanon to Dragon Ball.