Any differences in killing processes by these two approaches?
Yes. In DDMS, "Stop Process" kills the process. With "Force Stop", not only is the process killed, but it is moved into the "stopped" state, where nothing in that app will run again until somebody manually runs one of that app's components (typically: the user launches an activity from the home screen).
You can read more about the stopped state in the Android 3.1 documentation.