algophobia vs simple phobia

algophobia and simple phobia both are nouns.

Word	Noun	Adjective	Verb	Adverb
algophobia	Yes	No	No	No
simple phobia	Yes	No	No	No

As nouns, simple phobia is a hypernym of algophobia; that is, simple phobia is a word with a broader meaning than algophobia:

algophobia: a morbid fear of pain
simple phobia: any phobia (other than agoraphobia) associated with relatively simple well-defined stimuli

algophobia (noun)	simple phobia (noun)
a morbid fear of pain	any phobia (other than agoraphobia) associated with relatively simple well-defined stimuli