logician vs syllogist

logician and syllogist both are nouns.

Word	Noun	Adjective	Verb	Adverb
logician	Yes	No	No	No
syllogist	Yes	No	No	No

As nouns, syllogist is a hyponym of logician; that is, syllogist is a word with a more specific, narrower meaning than logician:

Other hyponyms of logician include dialectician, syllogiser, syllogizer, symbolic logician.

logician (noun)	syllogist (noun)
a person skilled at logic	logician skilled in syllogistic reasoning