I'll start with the OGP definitions:
- Geographic. A coordinate reference system based on a geodetic datum and using an ellipsoidal (including spherical) model of the Earth. This provides an accurate representation of the geometry of geographic features for a large portion of the Earth’s surface. Geographic coordinate reference systems can be two- or three-dimensional. A Geographic 2D CRS is used when positions of features are described on the surface of the ellipsoid through latitude and longitude coordinates; a Geographic 3D CRS is used when positions are described on, above or below the ellipsoid and includes height above the ellipsoid. [...]
- Geocentric. A coordinate reference system based on a geodetic datum that deals with the Earth’s curvature by taking the 3D spatial view, which obviates the need to model the curvature. The origin of a geocentric CRS is at the centre of mass of the Earth.
In practice, I would identify the difference between, say, a Geographic-3D and a Geocentric CRS in the fact that the latter has a central point in the 3D space from which angles and elevation are computed (no ellipsoid is needed, Earth is spherical?), whereas the former refers to the datum/ellipsoid, i.e. latitudes, longitudes and heights are computed with respect to the ellipsoid.
Am I saying something wrong or missing something? Thanks.