thirty-seventh vs 37th

thirty-seventh and 37th both are adjectives.

Word	Noun	Adjective	Verb	Adverb
thirty-seventh	No	Yes	No	No
37th	No	Yes	No	No

As adjectives, thirty-seventh and 37th are synonyms defined as:

thirty-seventh and 37th: the ordinal number of thirty-seven in counting order

thirty-seventh (adjective)	37th (adjective)
the ordinal number of thirty-seven in counting order	the ordinal number of thirty-seven in counting order