The direction that an (air)plane or a (sea)ship is pointing to is called heading:
the compass direction in which the longitudinal axis of a ship or aircraft points
The direction that an (air)plane or a (sea)ship is moving is called course:
the direction of travel of a vehicle (such as a ship or airplane) 1
Heading and course can be different when there is wind (or when there is a water current in the case of a ship).
"Heading" and "course" are expressed in cardinal directions (i.e. "north/south/west/east") or degrees of rotation relative to the north (e.g. "heading 90 degrees" and "heading east" are synonyms). These are measured on a horizontal (geometric) plane, (i.e. a surface which is perpendicular to the direction of gravity).
The "up/down" direction that an airplane is pointing to relative to the horizontal plane is called pitch angle:
The pitch axis [...] has its origin at the center of gravity and is directed to the right, parallel to a line drawn from wingtip to wingtip. Motion about this axis is called pitch.
The "up/down" direction that an airplane is moving relative to the air around is called angle of attack:
[...] the angle between a reference line on a body [...] and the vector representing the relative motion between the body and the fluid through which it is moving.
The "up/down" direction that an airplane is moving relative to the ground is called angle of climb:
The angle of climb can be defined as the angle between a horizontal plane representing the Earth's surface and the actual flight path followed by the aircraft during its ascent.
Note that the angle of climb depends on the ratio between horizontal distance traveled and the change in altitude, which is usually relative to mean sea level (I say "usually" because there is more than one way to define what "zero altitude" means).