In most simple terms
INS knows where it isn't and using interpolation tells the operator where it must be by process of elimination.
IRS constantly tracks its known position and reports that.
INS can not be updated in flight although the computer can be updated to provide an adjusted assumed position (vor/dme/tacan updating) up until the error correction region limit is exceeded. Then it dumps.
IRS can be corrected but not reinitialized in flight. There is no limit to the amount of error correction so dumps without an accelerometer failure are very rare.
INS knows where it isn't
IRS knows where it is
DME/GPS removes the error in the Navigation computer which today is most commonly the FMS but used to be (not so long ago) in the INS.
Don't confuse FMS with INS/IRS
FMS uses what it's told to navigate with.
You guys are really making me feel my gray hair.
