I'm unclear, and monolingual Japanese dictionaries aren't clarifying for me. My current assumptions are: (1) ドライブ seems to only mean driving an automobile, while 運転 can mean driving any type of vehicle. (2) ドライブ seems to usually mean driving for fun, although I've also seen it mean to drive somewhere for a specific purpose. (3) ドライブ seems to emphasize the act of you moving yourself places via a vehicle, while 運転 seems to emphasize the act of you operating the vehicle.
Which of these assumptions are correct/wrong, and are there any other nuances I'm missing?