hostel vs student lodging

hostel and student lodging both are nouns.

Word	Noun	Adjective	Verb	Adverb
hostel	Yes	No	No	No
student lodging	Yes	No	No	No

As nouns, hostel and student lodging are synonyms defined as:

hostel and student lodging: inexpensive supervised lodging (especially for youths on bicycling trips)

Other synonyms of hostel include youth hostel.

hostel (noun)	student lodging (noun)
inexpensive supervised lodging (especially for youths on bicycling trips)	inexpensive supervised lodging (especially for youths on bicycling trips)
a hotel providing overnight lodging for travelers