stenographer vs shorthand typist

stenographer and shorthand typist both are nouns.

Word	Noun	Adjective	Verb	Adverb
stenographer	Yes	No	No	No
shorthand typist	Yes	No	No	No

As nouns, stenographer and shorthand typist are synonyms defined as:

stenographer and shorthand typist: someone skilled in the transcription of speech (especially dictation)

Other synonyms of stenographer include amanuensis.

stenographer (noun)	shorthand typist (noun)
someone skilled in the transcription of speech (especially dictation)	someone skilled in the transcription of speech (especially dictation)