logician vs syllogizer

logician and syllogizer both are nouns.

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

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

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

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