Well, therapist is a modern coinage, along with the slightly older therapeutist. In Greek, there were two nomina agentis for therapeuo ' to treat medically; serve': therapeutes and therapeuter (with a feminine form therapeutris). Another discussed the -ism / -ist and -asm / -ast suffixes. Intersting that there isn't a therapism. The verb stems from a noun theraps 'a servant or companion'. There is also a theory that it is a loanword from Hittite.