Well, I think most people use trad and anaon for two different things: though they overlap, because trad generally includes anon, but anon doesnt generally include trad.
Trad is used to refer to songs which are passed on from person to person, often aurally, and are usceptible to change, and are not generally considered to be the product of a specific composer. Anon may be an obviously composed arts song, not susceptible to the oral traditional, but it just so happens that nobody knows the author.
"Trad" is a category that sticks: once you're trad, you stay trad. But you're only "anon" till some smartarse PhD student comes along and discovers the copy signed by the composer in the British Museum.