You're describing a current without actually using the word current. Guess what happens when you have potential differences and a conductor. A current. It's literally the definition.
Smooth, skeletal and cardiac muscle cells and nerve cells do have some differences in their respective ion channel compositions. As a result, their action potentials will look somewhat different. And obviously muscle cells contract while nerves do not. Those differences aside, they are all are excitable tissues. Importantly, they all have voltage-gated ion channels. So they all will respond similarly when placed in electric fields.