Ritual and ceremony are synonyms for rite

The difference between rite and ritual are not easy to explain and define as it seems that the rite is the archeotype for any possible ritualization and the ritual is the concrete local experience of the rite.

It is the Nacirema ritual of brushing your teeth.

One would use the word 'rite' in a sentence when referring to a religious or customary observance or if you were using ritual, that could be used as a routine like " in my ritual morning I took a shower