I try to answer, correct me if wrong
You activate the key under the battle.net account, and the in game character are created under the battle.net account that you logon.
Character are also server base, if u change server (Eg: from US to ASIA server), ur character didn't move over and you have to create new character for other server (under same battle.net account).
Thus, the character are tie with ur battle.net account.
You can play ur character at any places as long as u have the diablo installed and internet connection. But, you can't use ur friend activation key (which assume here, under another battle.net account).
If you use other account, mean another user logon with different character.

Hope it make you clear....