What is the difference in a tile-in & undercounter kitchen sink? I think they installed wrong sink in my new home. The granite overhangs a little. Shouldn't it be flush in undercounter installation? If they installed a tile-in would there be some overhang?

Installation method for undermount sinks vary among manufacturers. There are many different installation methods depending on style of sink. Not all sinks are flush with slab. If you have some overhang of slab, then you have a recessed installation.