Welcome to FT!
In general F = first class, J or C = business class, Y = coach. Someone might use the three letters instead of writing out "first class", "business class" or "coach". On the other hand these also represent the full-fare booking class for each of the classes, respectively, which may lead to confusion.

"I bought a ticket in Y" should read "I bought a ticket in coach"
"I bought a full-Y ticket" should read "I bought a full-fare ticket in Y booking class"

Hopefully this clears things up a bit.