The Magnavox Odyssey was introduced in 1972. It was a fairly primative video game system that used card-like cartridges and screen overlays. The controllers were boxes with knobs on the sides and a "Reset" button on the top. A complete Odyssey set includes stuff like poker chips, game playing cards, and other accessories. I had one of these back in the late 70's and it was pretty nifty.
The Magnavox Odyssey2 was introduced in 1978 and is comparable to an Atari 2600 technology-wise. It has a membrane keyboard and hard-wired joysticks (I'm not sure of all O2's had the sticks hard-wired, though...mine does) and used cartridges for games (the Magnavox carts have loop handles). Games for the console include K.C. Munchkin! (a good Pac-Man clone), Pachinko! (Magnavox put exclamation points in quite a few of the game titles for some reason), and Turtles. There are a few (fairly rare) third-party titles for the console (like Parker Bros. Popeye and Imagic's Demon Attack and Atlantis).
The two consoles have absolutely nothing to do with other besides the "Odyssey" name. The "2" on the name Odyssey2 is usually printed as a superscript (like Odyssey-to-the-second-power).