You can identify your crankset using the model number on the inboard side of the crank at the pedal hole (4500-series are Tiagra, 5600-series are 105), or by the fact that the 105 cranks are hollow, whereas the Tiagras are just channeled on the inboard side. The 105s also say "105" on them, and the Tiagras say "Tiagra."

The 50-tooth chainring in your second link will not work on a compact because it has the un-compact 130mm bolt-circle diameter. You need 110mm BCD.