philosophy vs axiology

philosophy and axiology both are nouns.

Word	Noun	Adjective	Verb	Adverb
philosophy	Yes	No	No	No
axiology	Yes	No	No	No

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

philosophy: the rational investigation of questions about existence and knowledge and ethics
axiology: the study of values and value judgments

philosophy (noun)	axiology (noun)
the rational investigation of questions about existence and knowledge and ethics	the study of values and value judgments
a belief (or system of beliefs) accepted as authoritative by some group or school
any personal belief about how to live or how to deal with a situation