In episodes 63-65 of the Boruto anime, Momoshiki Ōtsutsuki's Rinnegan has changed its color, compared with the color of the usual Rinnegans or from the movie Boruto: Naruto Next Generations? Could this mean Rinnegan also has variations?
Yes, Rinnegan has variations especially that of Momoshiki's where it is depicted in different colors:
Momoshiki Ōtsutsuki has a pair of Rinnegan embedded in the palms of his hands. They are initially red, but after he consumes his guardian, Kinshiki, they become purple (in Boruto: Naruto the Movie) or yellow (in Boruto: Naruto Next Generations). This also grants him a third Rinnegan on his forehead, which matches the other two in colour. In the anime, Momoshiki's yellow Rinnegan temporarily turn red when he uses their power.