Windshear and GPWS aural alerts are totally independent of one another.

"(2 beeps), Windshear, Windshear!" is annunciated when the aircraft's windshear detection system indicates a windshear in progress. Some aircraft are also equipped with predictive windshear warning systems, which will annunciate (depending on model) "Caution, windshear ahead!" or "Caution, microburst ahead!"

GPWS aural warnings operate off a totally separate system which makes use of, among other things, data from the aircraft's radio altimeter, vertical speed indicator, pressure altimeter, IRS units, and in some cases, EGPWS. This system generates the warnings such as "Sink rate!" or "terrain... whoop whoop, pull up!" These warnings are different and may vary from airplane to airplane, obviously.

The reason you hear the windshear and GPWS warnings together sometimes when boarding is because it's standard procedure to test the GPWS, and (at least in Boeing aircraft), pressing the GPWS test button tests the windshear warning system at the same time, normally: "Terrain, terrain... whoop whoop, pull up....... windshear, windshear!" (in that order).

You'd never want to hear all three of those warnings at the same time on an airplane you were flying.