skin rash vs eruption

skin rash and eruption both are nouns.

Word	Noun	Adjective	Verb	Adverb
skin rash	Yes	No	No	No
eruption	Yes	No	No	No

As nouns, eruption is a hypernym of skin rash; that is, eruption is a word with a broader meaning than skin rash:

skin rash (noun)	eruption (noun)
any red eruption of the skin	the sudden occurrence of a violent discharge of steam and volcanic material
	a sudden very loud noise
	the emergence of a tooth as it breaks through the gum
	a sudden violent spontaneous occurrence (usually of some undesirable condition)
	(of volcanoes) pouring out fumes or lava (or a deposit so formed)
	symptom consisting of a breaking out and becoming visible