Do I have to say if the face-down card I'm playing is a trap or spell, or is it enough to place it in the trap/spell zone?
You do not have to state if it is a spell or trap card when you set a card face down, it just must be legal in the zone you are setting in. This is actually done with spell cards to bluff traps and make your opponent pause to think about what you could have, and what it could mean for them with their plays.