*cough*
It's trade, not trad. You publish to the book trade, or you self-publish (also perfectly legitimate and an excellent choice) or you can legitimately vanity publish as long as you know that that's what you're wanting to do - and why. But trad-publishing is not a thing. You can't publish to a trad because there's no such thing, and you can't really publish to a tradition. That would mean something different.
Per the AW Dictionary -
This is off-topic, SORRY!
You're technically correct, of course -- but you're tilting at windmills.
Trade Publishing IS the term for what most major publishers do -- books that sell into bookstores are generally speaking "Trade", I sell into the Trade market (as opposed to the Educational market, or the Religious market, both of which are vast and their own things with their own imprints/publishers, different rules and expectations, etc) -- while there's a LITTLE crossover between these markets, the vast majority of books you see at B&N are Trade books from Trade publishers, and that's usually the kinds of books we are talking about on this type of forum.
I'll go further -- "Indie"
for a publisher means "an independently owned publisher" -- ie, a publisher that is NOT owned by a major multinational corporation -- rather than "self-published".
That being said: This semantic battle is lost, I'm afraid -- since many MANY self-published authors identify as "indie authors" or say that they are doing "independent/indie publishing", and identify the opposite of that as "traditional publishing" -- I think we have to accept that this has entered the lexicon when referring specifically to self-vs-not-self publishing.