The RAD child doesn't want to do it. The ODD child can't do it.
This is a great way to think about it.
The two go hand in hard and often seen together. RAD is about attachment and relationships. ODD is more of a PTSD reaction. So the difference is in the root cause, not so much the behaviors.
A RAD child will fight because they are scared of relationships. They don't want anyone to be in control of them.
An ODD child fights because something triggers the "fight or flight" response in them. Again, it may be about control in that you ask them to do something and it triggers in them that when someone else is in control, it is harmful. So they fight.
It is hard to tell them apart. And they are very entwined. The biggest thing - is it in response to a relationship? If so, its RAD based. This is why RAD kids are so much worse at home. They are reacting to a relationship. In school, there is no real relationship expectation. If its ODD, it will come out everywhere.
Does that make any sense? I kind of rambled....