Both altitude and elevation are measures of the height of a point relative to some datum. The differences are in how they are derived and what they are normally used for.
Altitude is typically only used to describe the height of an aircraft in flight. It is a barometric measurement expressed relative to the height of a runway or mean sea level in a given location or region (taking into account current local atmospheric conditions), or to an arbitrary standard datum (to eliminate the effect of localised variations in air pressure).
Elevation is usually used to describe the height of the ground, or a feature fixed to the ground. It is a geometric measurement expressed relative to the mean sea level datum established for the region by the national mapping agency.
I would take some care to understand the meaning of a value named altitude obtained from a GPS receiver. At a basic level, GPS can only tell you the receiver’s height above the WGS‑84 ellipsoid, and it cannot be assumed that the surface of the ellipsoid is the same as mean sea level in any given location. Some receivers contain look-up tables to calculate the offset between the two, given a lat/long position, which ought to be incorporated in the determination of ‘altitude’.
Whether to use altitude or elevation for your application is largely a matter of preference, I’d say. Since a moving car is neither an aircraft in flight nor fixed to the ground, I’ve conveniently excluded it from my definitions of the two terms here. As your measurement is geometric rather than barometric, I’d lean towards elevation. Alternatively, you could just keep the terminology simple (if imprecise) and call it height…