To me, the word "theodolite refers to an instrument that is used for surveying. I agree with the previous post that it does measure angles, both vertical and horizontal. However, at least as we use the term in the US, theodolites are not used in airplanes -- they are used in surveying. They are the piece of equipment that one surveyor looks through while the other holds a pole up to give the first one something to sight on. By doing this from a variety of points and angles, the surveyors are able to map out a given area.
Theodolite is a measuring instrument, that is also called altimeter.
Theodolite is an instrument for measuring horizontal angles (angle from zenith) and vertical (vs. horizontal),and it is used in geodesy and mining. The instrument is equipped with a graduated eyepiece telescope which helps the operator for precise targeting of a point to the ground.
Altimeter measures the altitude (height) above a reference level (not necessarily sea level), and it could be found on board of the gliders and aircrafts.