Obi,
Think there's a lot of confusion with some of the retrofit & older systems. On any aircraft post Boeing 757/767 - 737NG, & most Regionals the same Attitude/Heading system (whether AHRS or IRS boxes) provides identical but seperate databuses (generally ARINC 429HS) to both the Displays and the Flight Guidance/Control Computers - usually split Onside displays, onside FCC & Offside Display (for reversion). Pitch, Roll & Heading plus their appropriate rates & accelerations are all on the same bus. IRS also provide both body & flight path referenced data hence their use on HUDs and also Latitude & Longitude. INS is only a relatively simple FMS grafted onto an IRS to provide a navigational function - nowadays most aircraft fit a completely seperate FMS with much more functionality & using GPS for primary position.
All Part 121 & 91 aircraft now also have to carry an FDR system one element of which is a dedicated Triaxial Accelerometer mounted close to the aircraft center of gravity that is used to reconstruct the aircraft flight path in the case of an incident.