inference vs derivation

inference and derivation both are nouns.

Word	Noun	Adjective	Verb	Adverb
inference	Yes	No	No	No
derivation	Yes	No	No	No

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

inference: the reasoning involved in drawing a conclusion or making a logical judgment on the basis of circumstantial evidence and prior conclusions rather than on the basis of direct observation
derivation: a line of reasoning that shows how a conclusion follows logically from accepted propositions

Other hyponyms of inference include analogy, corollary, deduction, entailment, implication, extrapolation, presumption.

inference (noun)	derivation (noun)
the reasoning involved in drawing a conclusion or making a logical judgment on the basis of circumstantial evidence and prior conclusions rather than on the basis of direct observation	the act of deriving something or obtaining something from a source or origin
	drawing off water from its main channel as for irrigation
	drawing of fluid or inflammation away from a diseased part of the body
	inherited properties shared with others of your bloodline
	a line of reasoning that shows how a conclusion follows logically from accepted propositions
	(historical linguistics) an explanation of the historical origins of a word or phrase
	the source or origin from which something derives (i.e. comes or issues)
	(descriptive linguistics) the process whereby new words are formed from existing words or bases by affixation