Bas-relief vs incised
Even after looking at tons of Egyptian carvings in photos and in books, I was still interested to see the differences between bas-relief carving and incised carving.
Bas-Relief is done by removing the *background* of the picture, leaving the figures and writing standing above it, making them looked vaguely (or strongly) embossed. We never saw any examples of the extreme form of bas-relief - () - that is occassionally seen in Rome, where the figures are nearly three dimensional and stick out from the background as if emerging from the wall. I dont' think that is a style that is used at all in Egyptian art.
Incised carving is sunken in -- the figures are still carved normally (not inversed, or curved in), but are sunk into the wall. It's a very different look. In some cases, things are sunk in less than ain inch, just enough to allow the figure to be carved. Others, like our friend Ramses II, carved his stuff in several inches to ensure that no one could get rid of them. It's startling sometimes -- in some casees he hieroglyph for Ra (just a simple circle) is carved in like a tube.
Obviously bas-relief takes much longer to perform than incised carving -- removing the background in addition to shaping he figures simply takes more time. However, there are more concrete reasons for the different kinds of carving.
Outside, where wind and sand and possibly rain would hit the carvings, they were sunk in to protect them. If the carvings are incised an inch or so, they are somewhat protected from the ravages of weather, especially if they were painted. In some cases, you can still see tiny bits of paint that remain in the deeper parts of the carvings.
Inside, in protected halls and temples, the more delicate bas-relief was used (at least for a while.) There was little risk of them being blasted by sand, so the finer work was performed inside. Paint wasn't scoured off the stone by millenia of wind and sand, so the reliefs inside are often still beautifully colored.