Might I suggest that in fact they are both part of the same.
INS = Inertial Navigation System, a nav system that uses acceleration information from an inertial reference system to provide through computation in all 4 axes a position in space from a predetermined point. In the terrestrial case the surface of the earth
IRS = Inertial Reference System is the actual inertial platform that measures the acceleration inputs in all axes that provides the means of measurement and computation to the INS. This can be gyro (either free or strapdown) or ring laser. This measurement is relative to a starting point in space, therefore the INS must be oriented and aligned with the grid along which it must provide navigational information. In our case reference earth and Lat and Long. This is why it is necessary for the sytem/aircraft to remain stationary for a period of time on system start up to set reference zero acceleration within the IRS and allow alignment with the navigation grid and reference time. The old gyro systems may have taken up to 60 minutes to align with the modern ring laser only minutes.
FMS use a combination of available land based navaids, IRS and ultimately GPS to arrive at the most accurate position available by crosscheck.
As they all have differing degrees of accuracy over time and area the mode that is available or being used is always annunciated.