No they are not. The Jolly Green Giant is a mascot for Green Giant vegetables. Jack and The beanstalk is a fairy tale although the Jolly Green Giant does look like a beanstalk.
The giant's name is never mentioned in Jack and the Beanstalk. In "Jack the Giant Killer" the giant's name is Blunderbore. Alson in "The Thief and the Beanstalk" mentioned the the wife of the giant...