Maybe there are other definitions, but the way I’m using the term, what you described would definitely be an agent. An oracle probably wouldn’t have an internet connection at all, i.e. it would be “boxed”. (The box is just a second layer of protection … The first layer of protection is that a properly-designed safe oracle, even if it had an internet connection, would choose not to use it.)
Maybe there are other definitions, but the way I’m using the term, what you described would definitely be an agent. An oracle probably wouldn’t have an internet connection at all, i.e. it would be “boxed”. (The box is just a second layer of protection … The first layer of protection is that a properly-designed safe oracle, even if it had an internet connection, would choose not to use it.)