freshman vs first-year

freshman is a noun but first-year is not a noun.

Word	Noun	Adjective	Verb	Adverb
freshman	Yes	Yes	No	No
first-year	No	Yes	No	No

As adjectives, freshman and first-year are synonyms defined as:

freshman and first-year: used of a person in the first year of an experience (especially in United States high school or college)

freshman (noun)	first-year (noun)
a first-year undergraduate
any new participant in some activity

freshman (adjective)	first-year (adjective)
used of a person in the first year of an experience (especially in United States high school or college)	used of a person in the first year of an experience (especially in United States high school or college)