Does the tailplane have a positive/negative camber?
The tailplane should produce less lift than the main wing, for pitch stability. That is to say, its lift is negative relative to the wing lift. Its lift need not be wholly negative (pointing down), although it usually is during takeoff and landing.

But yes, as a first approximation, the direction of camber matches the direction of lift.

Also yes, negative lift (at the tail or anywhere else) can be called downforce (at the tail or anywhere else).

Here is Peter's explanation.