The part under the seat is called the
BOWL the space where water and other stuff goes down the drain is called the
Now i doubt there is a technical name further than that and In the building trade we always set a toilet on the Bowls Base, so the top will be the Bowl Head( which in your case is what you are referring to as the "Lip") and on the head you mount the Seat.
What you have circled is called the toiled mounting. The screw you use is called a mounting screw and the mounting screw holds the Toiled base via the toilet mounting to a floor flange.Sometimes in between the base and the flange you can have a leak pan connected to another waste pipe.
If you have any more doubts.. please research this interesting document.