On February 25, 1972, the anthology series aired a segment titled Love and the Television Set (later renamed Love and the Happy Days for syndication after the actual series debuted), which told the story of Richie Cunningham, his family, and friends.
The premise and characters were later used for the 1974 television series Happy Days. The original 1972 series was considered to be the pilot for the new show.
So, technically, Happy Days predates American Graffiti by a couple of years.
There are more connections. George Lucas cast Ron Howard in the film partly because of his performance in that original pilot.
Also, the success of American Graffiti actually caused ABC to reconsider the pilot for a full series order. They even did their best to connect the series to the film as much as possible, with similar titles fonts and music as well. This is what led many people to believe that the series was a spinoff of the movie. It was not.
However, Happy Days had some major hit spinoffs of its own.
Laverne and Shirley
RIP Bucky - 7/25/1943 - 1/19/2013