A celebrant is someone who officiates at a rite or ceremony. It is specifically for someone presiding over the Eucharist, a bread and wine sacrament.
A celebrator is someone who celebrates or recognizes a special event by having a party or some other unique activity.
As a side note: the adjective form of celebrate is celebrative and one definition of celebrate is to officiate or perform a rite.
In the United States celebrant is an accepted synonym for celebrator. This accepted usage is sometimes found in other English-speaking countries as well. However, caution should be used and, when in doubt, keep the distinction intact.
Examples
Businesswoman and civil celebrant Judy Mansfield has donated £600 to the British Heart Foundation. [Banbury Guardian]
The service for the couple, who have been together for six years, would include two celebrants, 400 guests, a hangi, a marae sleepover, a lakeside backdrop and possibly some booming Eminem rap music. [Stuff]
“Trying to get in the Christmas spirit,” said one celebrant downtown.[WTHR]
Stormy weather sent celebrants indoors but did not dampen their joy in celebrating the Mimouna at the end of Passover in Israel. [The Jewish Press]
Patti seems unsurprised by that revelation (who is, really?) and says she was never a spring break celebrator either. [The Wall Street Journal]
The LBPD urges all celebrators, bar hoppers and party goers to designate a sober driver ahead of time or have a concrete plan of traveling home safely to avoid disaster. [Long Beach Post]