INS navigates (tell it where you want to go and it will tell you how to get there - usually via the flight director and almost always can be coupled to the autopilot. The heading and attitude outputs are a useful by product of the stable platform (either virtual or physical) used to supply the navigation circuits with groundspeed and direction information) The system is stand alone.
IRS only supplies reference information (attitude, heading, speed, acceleration, etc,etc,etc. This is then fed to other systems which calculate a navigation solution (FMGS) or display the output as a compass rose or attitude ball.) The system cannot navigate, it can only provide present position information.
The details of the internal mechanisms are irrelevant(IRS not always solid state). There are INS's that use RLG's and IRS's that use standard rate gyros.