Some American English speakers use these words interchangeably.

Problem:
These two nouns are not synonyms.

Explanation:
Both of these nouns are often applied to habitual behaviors seen in athletes.

While watching a televised event from the 2008 Olympics, I heard the TV commentator call one of the athletes’ behaviors a “superstition”, but I saw the behavior as a “ritual” instead.

The definition of “ritual” as it applies to habitual behavior is a pattern of behavior that regularly occurs in a defined manner.

The definition of “superstition” as it applies to habitual behavior is an act based on a belief not based on knowledge or reason.

So, although superstitious behavior can be ritualistic, not all ritualistic behavior is superstitious.

A ritual for a tennis player could be focusing on the racket strings between points; a superstition for a tennis player could be always entering a tennis court from the north side.

In other words, a ritual can help an athlete to stay centered, whereas a superstition can unnerve an athlete when the athlete cannot perform the habitual behavior associated with the superstition.

Solution:
Use “superstition” for habitual behavior that is not based on knowledge or reason. Use “ritual” otherwise.