Most newer aircraft have built in Windshear warning sensors. They look like little wings near the nose on each side of the aircraft.
Pull up, Pull up is actually only modes 1 and 2, BUT all of the other modes (except 6 and 7) are interwined. Ie, If you get a glideslope deviation (usually low) you are "usually sinking to fast" (mode 1) and are too close to the ground (mode 2) (TERRAIN aural warning) . The intial callout will be a "glideslope" Aural warning twice, it can be a combination of "glideslope, PULL-UP" twice
Mode 4 will flash RED on the TCAS and have GROUND on the screen, it will be followed by PULL-UP twice )(mode 2)
Winsdhear DOES not call pull up, pull up.. Because in certain windshears you need to dive to regain airspeed. The Aural warining is Windshear twice followed by command bars indicating the path of travel to take as well as a visual warning (in yellow) on the EFIS of "Windshear".
If there is Windshear in the vicinity of the airport, it is reported well in advance of landing or takeoff (landing is more critical) and it is ground based. Secondly, upon landing a pilot will report airspeed deviation and altitude of deviation to the tower who will report it to all other aircraft. Ie, An A320 reported +/- 15 kts, 250-350'. Not all airports have windshear advisory systems, so each aircraft upon landing can and will usually report windshear advisories.
Mode 6... gives the pilots a call out at specific heights above ground, the minimum altitude and several others.
Generally, ANY PULL UP or TERRAIN aural warnings that are not in visual conditions automatically warrant a go around. If a crew are in visual conditions (usually DAY only) they can choose to ignore and continue the approach. At some airports you will get "false" warnings on some approaches.