Both are NSAIDs. But. Asa has a 14 day effect on platelet coaguability. Ibuprofen has this effect only as long as it is in the blood stream. Asa has an effect caused by de-acetylation, on thromboxane synthesis by the lining of blood vessels , which inhibits atherosclerosis. This effect does not occur with nsaids other than asa, which may slightly increase it's risk. All may decrease arthritis pain, but asa is unique.
See below. Aspirin is a nonsteroidal anti-inflammatory drug (nsaids), but differs from most other nsaids in the mechanism of action. Though it, and others in its group called the salicylates, have similar effects (antipyretic, anti-inflammatory, analgesic) to the other nsaids and inhibit the same enzyme cyclooxygenase, Aspirin (but not the other salicylates) does so in an irreversible manner.