In astronomy, [declination is] the angular disance of a body north or south of the celestial equator. Declination and right ascension, an east-west coordinate, together define the position of an object in the sky. North declination is considered positive and south, negative. Thus, +90 degrees declination marks the north celestial pole [near the North Star], and -90 degrees the south celestial pole.
In astronomy, gunnery, navigation, and other fields, [altitude and azimuth are] two coordinates describing the position of an object above the Earth. Altitude in this sense is expressed as angular elevation (up to 90 degrees) above the horizon. Azimuth, in astronomical measurement, is the number of degrees clockwise from due south (usually) to the object's vertical circle (i.e. a great circle through the object and the zenith). For nonastronomical purposes, azimuth (or bearing) is generally measured clockwise from due north.
[The zenith is the] point on the celestial sphere directly above an observer on the Earth. The point 180 degrees opposite the zenith, direclty underfoot, is the nadir. Astronomical zenith is defined by gravity, i.e. by sighting up a plumb line. If the line were not deflected by such local irregularities in the Earth's mass as mountains, it would point to the geographic zenith. Because the Earth rotates and is not a perfect sphere, the geocentric zenith is slightly different from the geographic zenith except at the Equator and the poles. Geocentric zenith is the intersection with the celestial sphere of a straight line drawn through the observer's position from the geometric center of the Earth.
Encylopeadia Britannica, 15th edition, 1986.