forty-fourth vs 44th

forty-fourth and 44th both are adjectives.

Word	Noun	Adjective	Verb	Adverb
forty-fourth	No	Yes	No	No
44th	No	Yes	No	No

As adjectives, forty-fourth and 44th are synonyms defined as:

forty-fourth and 44th: the ordinal number of forty-four in counting order

forty-fourth (adjective)	44th (adjective)
the ordinal number of forty-four in counting order	the ordinal number of forty-four in counting order