degree vs depth

degree and depth both are nouns.

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

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

degree (noun)	depth (noun)
a position on a scale of intensity or amount or quality	the extent downward or backward or inward
the seriousness of something (e.g., a burn or crime)	degree of psychological or intellectual profundity
the highest power of a term or variable	the attribute or quality of being deep, strong, or intense
an award conferred by a college or university signifying that the recipient has satisfactorily completed a course of study	the intellectual ability to penetrate deeply into ideas
a measure for arcs and angles	(usually plural) a low moral state
a unit of temperature on a specified scale
a specific identifiable position in a continuum or series or especially in a process