A "table" has a "tabletop." A "counter" has a "countertop." A "desk" has a "desktop." Each is, exactly as its name suggests, the "top" of the object, the big flat slab-like top piece that is the working surface. Usually, people just call it "the counter." Only when you are remodeling a kitchen, you distinguish between the "countertop" and the "counter." Often the countertop is supported by a cabinet with drawers, and often people will decide to keep the cabinet but replace the countertop. If you were admiring somebody's kitchen, and it was the beautiful granite countertop that caught your eye, you might say "what a beautiful countertop" because it is the countertop specifically that you like.

I think I call mine a counter 49% of the time, and a countertop 49% of the time. In the other 2% it gets called all sorts of things: the work surface; that thing over there; the whatsit; the slab (that's because my old mother used to call hers 'the slab' - rather like the butcher's slab).

The relatively long and narrow table that is attached to a kitchen wall is a "counter." The top horizontal work surface of the counter is the countertop. The "kitchen table" is a usually square or round table that stands on its own legs, and is not attached to the wall.