A fairly good answer Blue, and broadly speaking correct. The INS system you described would have been the old LITTON INS. The Delco carousel INS actually had the componants mounted on a rotating platform to reduce standing errors.
The one glaring error is the assumption that there are no motors or moving parts in an IRS which uses laser gyros. In fact there are 3. These are known as dither motors and are mounted on the individual laser gyros to prevent a phenominum known as laser lock, where a rotational movement will in fact not produce a change in the interference fringe pattern.
From my old days studying this was a favourite CAA "catch you out" question.
Apart from that there are infact modern INS's the main difference is as has been stated that an INS includes a navigation computer, whereas the IRS does not (the navigation is done by the FMC). It is again wrong to suggest that the INS gyro outputs were not interfaced with a/c systems the older 707/727/747 and some 737's picked off INS platform attitude and used it to drive the ADI's and HSI's