lay reader vs layman

lay reader and layman both are nouns.

Word	Noun	Adjective	Verb	Adverb
lay reader	Yes	No	No	No
layman	Yes	No	No	No

As nouns, layman is a hypernym of lay reader; that is, layman is a word with a broader meaning than lay reader:

lay reader: a layman who is authorized by the bishop to read parts of the service in an Anglican or Episcopal church
layman: someone who is not a clergyman or a professional person

Other hypernyms of lay reader include layperson, secular.

lay reader (noun)	layman (noun)
a layman who is authorized by the bishop to read parts of the service in an Anglican or Episcopal church	someone who is not a clergyman or a professional person