degree vs highness

degree and highness both are nouns.

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

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

degree (noun)	highness (noun)
a position on a scale of intensity or amount or quality	the quality of being high or lofty
the seriousness of something (e.g., a burn or crime)	a high degree (of amount or force etc.)
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