Technically, an ICBM is just another missile, but it can fly a very long distance and they can carry a heavy warhead, or even multiple warheads. Something in the 3,500 mile distance for range.
The name itself is kind of a misnomer in that if we are talking about something that can fly between Asia and Europe, you only need a range greater than zero since they are next to each other. I'm guessing the Inter-Continental part though originated from the rough range needed to get from Siberia to a good portion of the United States, or from western Europe to the U.S. east coast.