allergic eczema vs eczema

allergic eczema and eczema both are nouns.

Word	Noun	Adjective	Verb	Adverb
allergic eczema	Yes	No	No	No
eczema	Yes	No	No	No

As nouns, eczema is a hypernym of allergic eczema; that is, eczema is a word with a broader meaning than allergic eczema:

allergic eczema: eczema caused by an allergic reaction
eczema: generic term for inflammatory conditions of the skin; particularly with vesiculation in the acute stages

allergic eczema (noun)	eczema (noun)
eczema caused by an allergic reaction	generic term for inflammatory conditions of the skin; particularly with vesiculation in the acute stages