If you mean the parks and commons in London, then the difference is mainly historical - it depends on whether the land was once a park (originally a place where people went hunting) or commons (land which could be used by the public).

http://en.wikipedia.org/wiki/Common_land
http://en.wikipedia.org/wiki/Park#History

Today, parks are usually more formal, with flower beds, while commons are left as green fields or wooded areas. You might also find a park that is left natural, but you don't see really formally landscaped commons.