Interestingly in all the replies, nobody actually defined the acronyms:
AHRS - Attitude Heading Reference System
It gives you the attitude and heading of your aircraft, and nothing more.
IRS - Integrated Reference System
It gives you the attitude and heading of your aircraft, plus navigation information: integrating the reference systems.
Various manufacturers interpret these in their own ways, adding options and using different systems to provide the information as they see fit.
Anything with a compass and horizon ball has an AHRS, even a DC3: