The date of discovery refers to the specific period when a person realizes the existence of adverse physical effects of past incidents or accidents. A suitable example would be someone realizing that his/her back condition is a direct consequence of years in heavy manual work. That particular day when a connection to an existing physical condition is made becomes the date of discovery.
On the other hand, the date of the accident is the precise date at which a person's involvement in a singular incident or accident resulted in mild to severe physical injury. A suitable example is someone who experiences a herniated disk while lifting a product-laden crate at work. The particular day when the herniated disk injury occurred becomes the date of the accident.