In-ground would be in the ground like most pool you see, not inflated or anything, but actually built into the ground. Under-ground would be like underground where you wouldn't even be able to see it, but I don't think people really have those. And above-ground pool is the inflatable ones or just any pool that is not built into the ground.
Above ground is like a big tank that its built and filled up with water like in this picture. Beyond that, they work the same but the the above ground are cheaper to buy. It cost thousands of dollars to built and inground pool compared to above. All the cost in bringing in the machinery and all that concrete.
Maybe you meant In ground and above ground pool? In ground pools mean that a hole will be dig up and the pool inserted or built to fill that hole. Like in the picture.
Well in-ground pools are the pools that are mostly inflated while under- ground pools are built on the ground and are built in tiles.