With these sorts of questions, the issue isn't so much with the earth or the reference system, but with the definition of "real." Angular coordinates only make sense in an axiomatic framework, with reference to an origin and an axis. There are no straight lines or points in nature, of course. These are things that are only defined in the mind.
In the case of WGS84, angular coordinates are taken with respect to a reference frame that is anchored as closely as possible to the centre of the Earth, as measured by the orbits of satellites. The orientation of the frame is set by alignment with distant quasars. Basically, it's a hypothetical box with with a hypothetical centre, with the earth inside of it. Projected coordinate systems such as recent editions of NAD83 are realisations of this model, with adjustments to account for tectonic drift, etc. (In contrast to this geocentric coordinate system, you've probably learned about NAD27, in which the reference ellipsoid is anchored to the Earth not by its centre, but at a spot on the surface of the Earth in Kansas.)
Elevations in this framework are measured from the surface of an ellipsoid, then usually adjusted using a geoid model to represent the equipotential surface -- roughly, the elevation of the ocean surface, if it covered the whole planet. Elevations measured relative to the geoid are called orthometric heights.
Of course, it is impossible to measure, with infinite precision, the "real" position of anything on a dynamic rock in space the way you would expect to do in a pure math context. Everything is modelled, which implies compromise. Though the compromises get smaller all the time, the rate of improvement is slowing -- naturally, the closer you get to an unattainable "truth", the slower your progress becomes. All measurements and positions on Earth merely have to be good enough, just as NAD27 was good enough for the time and the region it was intended to represent.
