Many a/an + singular noun

What is the peculiar difference between

(a) many a boy
(b) many boys

5 many a something formal or old-fashioned a large number of people or things: Many a parent has had to go through this same painful process.
I’ve sat here many a time (=often) and wondered what happened to her.

I agree that “many a…” is somewhat formal, and is not used a great deal in conversation, but I would not call it “old-fashioned”