There is no "true version" of fairy tales. They are an oral tradition with a multitude of versions - for example Cinderella is known in dozens of different version from across the world, and in the oral tradition probably every narrator had their own version.
The Disney Cinderella is based on Charles Perrault's version which was actually published earlier than the Grimms version. Both are recorded from oral versions. Perrault does not have the cutting off of toes, but have a fairy godmother and a magic pumpkin which is not present in the Grimm version.
Disney put their own slant on the stories of course, just like any other retelling.
Indeed. The Grimm fairy tales also include "German" stories that were actually of French origin. At least some of their supposedly rustic native sources were Huguenots, i.e., French Protestants, who settled around Kassel where the Grimm brothers lived.
Personally I grew up reading (and rereading) the Andrew Lang Fairy Books. They hew to the Perrault version of Cinderella. It would not be surprising if Walt Disney read those growing up. They were immensely popular and included wonderful Art Nouveau illustrations of characters in the stories. H J Ford was the artist for many of them.
The Disney Cinderella is based on Charles Perrault's version which was actually published earlier than the Grimms version. Both are recorded from oral versions. Perrault does not have the cutting off of toes, but have a fairy godmother and a magic pumpkin which is not present in the Grimm version.
Disney put their own slant on the stories of course, just like any other retelling.