That's basically it but every school has their own differences. Get the catalog and look up the course requirements between the 2.
At Ohio State, you can either take Computer Science & Engineering or Electrical & Computer Engineering. So CSE is closer to CS, and ECE is closer to EE. I like this way better because both give you a little bit of both, plus a lot of either software or hardware, depending which you choose.
Plus, most schools let you pick a specialization within your major. At OSU, in CSE you an specialize in hardware systems, software systems, information systems, or individualized (you design your own specialization).
In ECE you can specialize in Electrical Engineering, Computer Engineering, and a couple others (I don't know for sure, I'm in CSE).
I'm sure other schools are slightly different.