doubting Thomas vs doubter

doubting Thomas and doubter both are nouns.

Word	Noun	Adjective	Verb	Adverb
doubting Thomas	Yes	No	No	No
doubter	Yes	No	No	No

As nouns, doubter is a hypernym of doubting Thomas; that is, doubter is a word with a broader meaning than doubting Thomas:

doubting Thomas: someone who demands physical evidence in order to be convinced (especially when this demand is out of place)
doubter: someone who habitually doubts accepted beliefs

Other hypernyms of doubting Thomas include sceptic, skeptic.

doubting Thomas (noun)	doubter (noun)
the Apostle who would not believe the resurrection of Jesus until he saw Jesus with his own eyes	someone who habitually doubts accepted beliefs
someone who demands physical evidence in order to be convinced (especially when this demand is out of place)	someone who is doubtful or noncommittal about something