Your hunch is correct. At-home charging tends to be the cheapest while supercharging is going to command the highest premium.
I live in SoCal which has high EV adoption with loads of chargers everywhere and off the top of my head.
Off-peak home charging costs about 7 cents / KWh. My car's battery has about a 71KWh capacity so that's about $5 for a full charge.
Super charging prices vary on the time of day and region, but let's pick the worse time. You'll see about a 20-40 cents charge / KWh. That will cost me about $15-30. You can see those prices go down if you're charging at good hours though. Tesla will have morning incentives for instance.
Supercharging costs are higher because:
* Supercharging stations (for Tesla) cost about 300-400k USD per unit.
* Electricity providers charge a premium for higher amps/volt service.
As far as I know, Tesla doesn't try to make a profit with chargers. They keep it close to cost.