telegraph operator vs telegrapher

telegraph operator and telegrapher both are nouns.

Word	Noun	Adjective	Verb	Adverb
telegraph operator	Yes	No	No	No
telegrapher	Yes	No	No	No

As nouns, telegraph operator and telegrapher are synonyms defined as:

telegraph operator and telegrapher: someone who transmits messages by telegraph

Other synonyms of telegraph operator include telegraphist.

telegraph operator (noun)	telegrapher (noun)
someone who transmits messages by telegraph	someone who transmits messages by telegraph