Quote:What is an Open Character?
Open Characters are stored locally on your own computer and, while you can set up games and chat over Battle.net, you cannot play these characters on a Diablo II Realm. In an Open Game, one player's computer is the game server, while the other players connect to it. Since Blizzard cannot be responsible for the locally stored characters, or the servers upon which the games are played, Open Games are more vulnerable than Realm Games to certain forms of manipulation and abuses by other players. The big advantage of Open Games, however, is that you can bring your Single-Player Characters onto Battle.net. You can play with your friends over Battle.net and then continue playing that character in Single Player as often as you want.

Can you play an Open Character over Battle.net?
Yes. However, you cannot play in games with Realm Characters.

What is a Realm Character?
Realm Characters are played exclusively on Diablo II Realms over Battle.net and cannot play in Single Player, Open, or TCP/IP games. A Realm is a Diablo II game server hub that is hosted and maintained by Blizzard. While playing on a Realm, your character is secure from many cheats, hacks, or other abuses that could occur in an Open Battle.net or TCP/IP game. Realm Characters are stored on a Diablo II Realm and can accessed from any computer when you log into Battle.net. There are several Realms on Battle.net, each located in a different part of the world. When creating a Realm Character, choose a Realm whose location is closest to you for the best play experience.