degree vs first degree

degree and first degree both are nouns.

Word	Noun	Adjective	Verb	Adverb
degree	Yes	No	No	No
first degree	Yes	No	No	No

As nouns, first degree is a hyponym of degree; that is, first degree is a word with a more specific, narrower meaning than degree:

Other hyponyms of degree include degree of a term, degree of a polynomial.

degree (noun)	first degree (noun)
a position on a scale of intensity or amount or quality	a degree of one
the seriousness of something (e.g., a burn or crime)
the highest power of a term or variable
an award conferred by a college or university signifying that the recipient has satisfactorily completed a course of study
a measure for arcs and angles
a unit of temperature on a specified scale
a specific identifiable position in a continuum or series or especially in a process