A normal site map is in a HTML format and is designed to be read by browser software such as Internet Explorer, Netscape or Firefox and to be viewed by a human reader.
A Google Site map is in an XML format and is designed to be read by Google's spider, i.e. not by a human reader.
Although both include similar information they are in completely different formats, neither of which is suitable for the other purpose, i.e. a Google Site map wouldn't be of much use if viewed in a typical web browser such as Internet Explorer and the standard site map would be complete nonsense as far as Google's XML site map spider is concerned.