What are these round pads on the bottom of a PCB?
As mentioned in some of the comments, these are test pads designed for use with a pogo-pin test fixture, also known as a bed-of-nails test fixture. These fixtures have a specially-shaped array of pogo-pins which press down and make contact with the test pads on the board under test: 




These test pads and the test points are probably used in different parts of the manufacturing process. For example, the test points may be used for board-level testing and the test pads may be used for system-level testing. Or, perhaps, the test pads are used for programming and/or debugging firmware, when the device under test is clamped into the bed-of-nails fixture.