The Medway Handyman wrote

My sat nav battery only lasts about half an
hour unless plugged into the fag lighter socket.

Mine lasts a lot longer than that on a charge.

I was told that the display screen is what consumes the power.

That's only part of it.

The sat nav has a touch screen, but you can touch it with anything - the
end of a pencil for example.

The smart phone (Samsung Galaxy Ace) can be used as a sat nav for hours
without appreciably draining the battery and also has a touch screen,
but you have to use a finger or special stylus - the end of a pencil
don't not work.

Can someone explain the differences in technology?

Phones have gone to a lot of trouble to maximise the time between
charges, because its not feasible to plug them into the fag lighter
socket much of the time. That involves minimising the power use
of everything in the phone and blanking the screen auto too.