A linear voltage regulator needs a certain voltage across it to operate. I believe (and I don't have any datasheets here right now) that a 78xx device needs at least 3V across it to operate reliably. So a 7805 for instance will only work (reliably) if the input voltage is 8V or more.
A low drop regulator like a 4805 will work reliably with a lower voltage across it, that is (again without a datasheet) with at least 1V across it.
So: if you have 6V, and you want to go to 5V, you must use a low drop regulator. If you have 9V and you want to go to 5V, it doesn't matter which one you choose technically, they will both do equally well.
In either case, P=U*I. The voltage actually dropped across the device times the current passing through it WILL be the amount of power dissipated by the device. In heat. Not light or sound.
Always be aware that it is foolishness to drop too much across a linear regulator in case you are talking about significant currents (>100mA). Going from 12V to 5V with a linear regulator at 1.5A of current, whether using a normal or a low-drop regulator is only serving to warm up our planet even further. Yep, I'm concerned about that.