Movie: Belle caused Gaston to fall out of the house into a mud pit.
Musical: Belle sneaks into the house while Gaston is doing his "Me" number and then closes the door, leaving him outside.
Musical tells you whey the servants were cursed into becoming enchanted objects. It was because they didn't do a good job raising Prince Adam prior to the Enchantress' arrival.
The movie didn't tell you why.
Movie: Gaston says he'll free Maurice if Belle marries him. Belle angirly says never.
Musical: Gaston says he'll free Maurice if Belle marries him. After that, he rudely kisses her (yuck!) Belle breaks the kiss, slaps Gaston on the face and shouts Never!