Unless you mean "sink (wash basin) in a bathroom," we do not usually say "toilet sink." If you are referring to the part that we sit on to do our business, we call it a "toilet bowl."
"Toilet sinks" also refer to toilet and sink combos, where the sink sits above the tank of the toilet so you can wash your hands while the reservoir is being refilled after a flush. See http://peswiki.com/index.php/Directory:Toilet-Sink_Combo
Here is a website with a labeled diagram of a toilet bowl and all its essential parts. http://www.toilet-repairs.com