Grease & Grudge (also known as Road Race) is a tech demo for a new racing game that was developed for the Panasonic 3DO, but they never released a title like that for the console. It is possible that this tech demo evolved somehow into Need for Speed, but for now it’s just a speculation. If you have more info about this demo, please let us know! Scans from Edge magazine 1 and 3.
Thanks to Pcloadletter and Celine for the contributions!