A water heater is basically just a tank that holds and heats water.
An electric water heater just has an anode rod, heating elements, thermostats etc in and on them.
A gas water heater has the gas valve, heating burner, and just a tank.
You can safely transport your water heater on it's side whether it's a gas or electric water heater.
No damage should occur by doing so. I've transported a few water heaters on their side before without harming them.