magnitude vs degree

magnitude and degree both are nouns.

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

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

magnitude (noun)	degree (noun)
the property of relative size or extent (whether large or small)	a position on a scale of intensity or amount or quality
relative importance	the seriousness of something (e.g., a burn or crime)
a number assigned to the ratio of two quantities; two quantities are of the same order of magnitude if one is less than 10 times as large as the other; the number of magnitudes that the quantities differ is specified to within a power of 10	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