Does the temperature you set your house thermostat at make any difference in the electric bill?

My son recently got a new AC installed in his house. As is his nature, he started researching How It All Works.

He was telling me that it doesn’t really matter what you have the thermostat set at. It’s summer, so if you have it set at 78, where I keep mine, it just keeps the house at 78. It simply kicks on when the thermostat reads 77 and blows until it hits 78 again.

Setting it at 76 doesn’t make a difference, because it just does the same thing. It just kicks on at 75, and kicks off at 76. It doesn’t blow colder air or anything. I’m thinking it’s how often it kicks on is the difference. But, then again, what he said kind of makes sense.
Does it take longer to get the house from 75 to 76 than it does to get it from 77 to 78?

I was shaking my head at him to tell him I thought he was full of crap, but, on the other hand, the logic was sound. He’s done that to me for as long as I can remember. He’ll just give me crap under the guise of a really good argument.

So, how does the temperature regulator work?