Hi Colaid. The Jaguar is essentially the child of the Jazzmaster. Their bodies are virtually identical, as sewkid's cool diagrams illustrate. The Jaguar was also the first Fender guitar with 22 frets, as opposed to the Jazzmaster's 21 frets. As gadabout mentioned, the Jazzmaster has the standard 25.5" scale length (like a Strat), while the Jaguar has a 24" scale length. Both have more complex switching than the Strat or Tele, creating an impressive variety of sounds. They are both well suited to surf music, but they are capable of much, much more. Both guitars have specially designed single-coil pickups, and those of the Jaguar have extra shielding.
Here are some sound clips from the Fender product pages:
American Vintage ‘62 Jazzmaster - http://www.fender.com/products//sounds/guitars/0100800.mp3
American Vintage ‘62 Jaguar - http://www.fender.com/products//sounds/guitars/0100900.mp3
I tested both guitars, and I found much to like about both of them. I ultimately chose the Classic Player Jazzmaster Special based largely on the standard scale length. I hope this helps!