All permanent split capacitor (PSC) induction motors are connected as shown in the picture below.
I added 4 colors to indicate each end of the main and auxiliary windings. Most PSC motors come with either 3 wires or 4 wires exiting the motor. For 4 wire PSC motors, the yellow, green, red, and blue wires exit the motor. Then they can be connected to the capacitor and power source as shown. Typically the main and auxiliary windings in a 4 wire PSC will be different (that is, they will have different number of turns, different wire gauge, etc.). That means that to reverse a 4 wire PSC, you need to switch the yellow and green leads around. This reverses the polarity of the main winding and causes the motor to reverse.
For 3 wire PSC motors, the main and auxiliary windings are identical (same number of turns, same wire gauge, but they are placed in different stator slots). Usually the red and green wires are connected internally so that only one wire exits the motor. When this is the case, the 3 wire PSC can be reversed in the same way as your second figure above. In my picture the switch would be in parallel with the capacitor and switch between the yellow and blue leads. This works because the main and auxiliary windings are identical and you are causing the main winding to lead or lag the auxiliary winding by switching.
3 wire PSC motors can be reversed with a single pole/double throw switch to reverse. 4 wire PSC motors require a triple pole/double throw switch to reverse.