In accordance with the international standard ISO 19111:2007, geographic information spatial referencing by coordinates, the following definitions are universally agreed upon:
A Coordinate Reference System (CRS) is a coordinate system that is related to an object through a datum. For geodetic and vertical datums, the object is the Earth.
A datum is a set of parameters that defines the position of the origin, the scale, and the orientation of a coordinate system.
A geodetic datum describes the relationship of a 2D or 3D coordinate system to the Earth.
A geoid is the equipotential surface of the Earth's gravity field that is everywhere perpendicular to the direction of gravity. The geoid best fits mean sea level either locally or globally. A geoid is considering the true shape of the Earth.
A projected coordinate reference system is a coordinate reference system derived from a two-dimensional geodetic coordinate reference system by applying a map projection.