There's some interesting stuff going on behind the scenes. GPS inherently gives you a 3-dimensional coordinate, which is useless for most applications. So the coordinate gets converted to a 2D surface coordinate (latitude/longitude) plus an altitude, which is what you generally want. However, since the Earth isn't a perfect sphere, this conversion is not well-defined.

The solution is a datum, a model of the Earth's surface that is used for the conversion. WGS84 is the datum used by GPS, and approximates the Earth as a specified ellipsoid. However, maps can use use different datums (data?), so there can be a discrepancy of many meters between what GPS says the location is, and what the map says the location is, and they can both be right relative to their datum.

> and an altitude above mean sea level

Nah, you're clearly misunderstanding how GPS works.

GPS allows you to directly measure displacement of any 2 points in 3 dimensions.

You're speaking of the altitude + lat/lon instead, which is in polar coordinates.