While rides may be "organized" in terms of start times, food stops, etc. they aren't timed for individuals. There's no first, second and third finishes. (I've done a number of rides, but no races.

Rides usually call themselves "rides" as in the "Ride for the Cure" or the "Wildflower Ride". Races do the same.

If you're interested in distance, but not necesarily riding faster than everyone else, go for a ride. If you want to compete then a race is for you. Centuries are usually rides. (except as J mentioned where people are going for personal bests or competing in small groups against their friends)

To complicate things there are different types of races like time trials, criteriums and stage races.