For aircraft, the horizontal stabilizer or tailplane is a fixed or adjustable surface from which an elevator may be hinged. In some aircraft models (mostly jets), the entire horizontal stabilizer rotates and functions as an elevator. This combination is often called a stabilator (see Cessna 177 or Piper Cherokee for light aircraft applications).
Aircraft with an adjustable stabilizer have the stabilizer hinged so that its setting (angle of incidence) can be altered in flight (see McDonnell Douglas DC-9 for an airliner application; see Cessna 180 for a light aircraft application). The resulting stabilized speed is known as the trim speed, and the trim is used to set the desired speed without having to hold the elevator out of its trimmed or faired (trail) position. In aircraft with truly fixed stabilators, a trim tab on the trailing edge of the elevator is used to alter the aircraft's trim speed (see Douglas DC-3 for an airliner application; see Cessna 172 for a light aircraft application). The F-86 Sabre first used a fixed stabilizer and elevators with a trim tab, but later versions used a stabilator.
A vertical stabilizer (also called a fin) is fixed to the aircraft and supports the rudder. The fin nearly always employs a small fillet at its forward base, called a dorsal fin, which prevents a phenomenon called rudder lock. Rudder lock is where the force on a fully-deflected rudder (in a steady sideslip suddenly reverses as the rudder reaches its maximum travel. NASA Flight Education website The phenomenon is usually corrected by addition of a dorsal fin. Princeton Aerodynamics Lecture Series
For aircraft with a V-tail, each stabilizer/fin will support a "ruddervator", combining the functions of both the rudder and the elevator.
The stabilizers (empennage or tail) provide stability while the aircraft is flying straight, and the airfoil of the horizontal stabilizer balances the forces acting on the aircraft.
While the vertical stabilizer and rudder are always placed on the rear of the aircraft (either on the aft fuselage, or at the ends of aft-swept wings), the horizontal surfaces can be placed on the front or the rear. When placed on the front, the aircraft is called a canard (see Beechcraft Starship for a large aircraft and Rutan Long-EZ for a small aircraft with this configuration). The Italian-designed Piaggio P.180 Avanti uses a rear-mounted stabilizer/elevator and a forward stabilizer (fixed, with no control surfaces); this combination arrangement is probably unique in present-day aircraft, although some early airplanes tried such arrangements.