These are taken from the USNO's Astronomical Almanac Glossary.
Another reference is the IAU's Nomenclature for Fundamental Astronomy
- Mean Position: coordinates of a star or other celestial object (outside the solar system) at a specific date, in the Barycentric Celestial Reference System (BCRS). Conceptually, the coordinates represent the direction of the object as it would hypothetically be observed from the solar system barycenter at the specified date, with respect to a fixed coordinate system (e.g., the axes of the International Celestial Reference Frame (ICRF)), if the masses of the Sun and other solar system bodies were negligible.
- Geometric Position: the position of an object defined by a straight line (vector) between the center of the Earth (or the observer) and the object at a given time, without any corrections for light-time, aberration, etc.
- Astrometric Position: the position of a solar system body formed by applying corrections for light-time displacement to the geometric position. This position is directly comparable with the catalog positions of nearby background stars after those positions have been updated for proper motion and parallax. There is no correction for aberration or deflection of light. It is assumed that these correction are nearly identical for both the solar system body and background stars.
- Proper Position: direction of an object in the Geocentric Celestial Reference System (GCRS) that takes into account orbital or space motion and light-time (as applicable), light deflection, and annual aberration. Thus, the position (geocentric right ascension and declination) at which the object would actually be seen from the center of the Earth if the Earth were transparent, non-refracting, and massless. Unless otherwise stated, the coordinates are expressed with respect to the GCRS axes, which are derived from those of the ICRS.
- Intermediate Position: the proper place of an object expressed with respect to the true (intermediate) equator and CIO of date.
- Apparent Position: the proper place of an object expressed with respect to the true (intermediate) equator and equinox of date.
- Topocentric Position: the proper place of an object computed for a specific location on or near the surface of the Earth (ignoring atmospheric refraction) and expressed with respect to either the true (intermediate) equator and equinox of date or the true equator and CIO of date. In other words, it is similar to an apparent or intermediate place, but with corrections for geocentric parallax and diurnal aberration. (See aberration, diurnal; parallax, geocentric.)
- Local Position: a topocentric place of an object expressed with respect to the Geocentric Celestial Reference System (GCRS) axes.
Not listed in the USNO's glossary, but useful is the Observed Position, which is the Topocentric Position, but
also accounting for atmospheric refraction.