based on [Voser 2007, p.106]

Coordinates are variables from the analytical geometry to describe positions in a coordinate system.

Coordinate Systems are geometric structure elements and reference systems for coordinates. Special coordinate systems are used in describing mathematically shape and size of geodetic earth models or in map projections.

Coordinate Reference Systems are coordinate systems in combination of a spatial datum to describe spatial position through spatial coordinates.

A spatial datum describes the position, size and orientation of a coordinate system regarding to the physical or geographical earth.