ducky vs teacher's pet

ducky and teacher's pet both are nouns.

Word	Noun	Adjective	Verb	Adverb
ducky	Yes	No	No	No
teacher's pet	Yes	No	No	No

As nouns, teacher's pet is a hyponym of ducky; that is, teacher's pet is a word with a more specific, narrower meaning than ducky:

Other hyponyms of ducky include chosen, macushla, mollycoddle.

ducky (noun)	teacher's pet (noun)
a special loved one	the teacher's favorite student