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According to online sources like wikipedia the difference belies on the addition of an on-board processing system (I assume it means a microcontroller) which outputs already processed data and not simply the raw measures of the different sensors.
However I would appreciate the take on this of someone who has experience on the subject, a more practical standpoint.
An INS calculates and updates the vehicle's position (latitude and longitude), alongside the orientation. It needs to be initialized on ground, with the aircraft completely still.
An AHRS does not record/update the position. It outputs real time orientation (attitude and heading) only. It thus can be initialized in flight.
Image shows the INS panel of a Boeing 747-400, notice the ATT (Attitude) option, that's an AHRS-only mode. NAV includes both AHRS and navigation.
ATT can be initiated in-flight, it requires a manual entry for the heading while flying straight and level. So in other words, an INS includes AHRS-functionality.
Sidenote on terminology: INS nowadays is predominantly used to describe an Inertial Platform, Inertial Reference System (IRS), and Inertial Reference Unit (IRU/IMU); and often used to describe all three of these units (as one system) typically installed on a single aircraft.
Ellipse2-A: Miniature AHRS
Ellipse2-A is a small-sized high performance Attitude and Heading Reference System (AHRS). It provides Roll, Pitch, Heading, and Heave data.
This light-weight sensor (45 grams) includes a MEMS-based Inertial Measurement Unit (IMU) integrating three gyroscopes, three magnetometers, and three accelerometers. Running an extended Kalman filter (EKF), the Ellipse-A provides accurate orientation data in both static and dynamic conditions.
So from this definition, the IMU is the sensor set in six Degrees of Freedom measuring in aircraft axes, and the AHRS provides roll, pitch, heading and altitude in earth axes. The difference is a set of axes transformations that is processed inside the unit.
From the same website:
Ellipse2-N is a small-sized high performance Inertial Navigation System (INS) with integrated GNSS receiver. It provides Roll, Pitch, Heading, Heave, and Navigation data.
So the difference between AHRS and INS is that the latter provides additional lat/lon data based on GPS co-ordinates which it obtains from a built-in receiver.
The classic 70s Inertial Navigation System in aircraft used very stable gyroscopes plus accelerometers to sense changes in 6-DoF in aircraft axes. These changes were integrated into positions changes and added to the reference position where the system was initialised. IRS systems pre-date the use of microprocessors, it used to be done by analog integrator circuits and other very clever analog stuff on printed circuit boards. However, the use of integrated signals means error accumulation, like sailors experienced when they integrated the knots velocity of their ropes into navigation position, and then crashed into the west coast of Australia due to accumulated position error.
So nowadays, not only are the spinning gyroscopes replaced by Ring Laser Gyro's, the position errors can be nulled by comparing the results with the GPS data. GPS data cannot be used directly for autopilot control due to the time lag in the signals. The inertia sensors provide results with a high frequency response, and integration errors can be nulled from the GPS and magnetometer signals.
