Im gonna use puss in boots as an example because it displays very clearly the difference between a villain, an antagonist and a rival.

Villain: A character whose evil actions or motives are important to the plot

Originally posted by imjulia-andilikecats

Antagonist: Someone who serves as an obstacle to the protagonist.

Originally posted by amazing--ace

Rival: Someone competing for the same objective as the protaginst

Originally posted by veronicawekilledourbabies

These roles CAN overlap but they can also exist separately.

a villain needs to commit evil. They dont need to see it as evil but their actions need to be evil in some way. jack in this example though, is unapologetically evil with no moral nuance

an antagonist can be any moral alignment, just serve to get in the way of protagonist. The wolf is morally neutral. he is a force of nature personified.

Rivals tend to be somewhat close in alignment as the protagonist to an extent and seek to get the same goal through similar or different methods that challenge the protagonist own skillset. goldilocks is not necessarily evil, but has the same ethics that puss and kitty display putting her on the same ground as the protagonist.