The difference is that a Google Site Map is there to help Google find its way around your site, and a regular site map is there to help both your customers and search engine robots to find their way around your site.

A regular site map is a page with a list of html links that index every page on your site that you want people to visit. They are particularly useful for search engines if you have (misguidedly) created internal links in an image or another format not supported by a search engine.

A Google Site Map on the other hand is a file attached to your website that is not designed to be seen by the public. It provides Google with full information about your site, so that Google can better crawl the pages. This helps Google keep up to date, and also ensures that your site gets the coverage that it deserves.

All the best

Huw