Which of the two buttons on the side of my Apple Watch is the power button?

Neither is called a “power” button. There is a crown and a side button. You can read more about the features of each bottom here:

Use the buttons and screen on your Apple Watch - Apple Support

If you are trying to find out how to power your watch off, here are the instructions:

1. Tap the crown.
2. Select Settings > General > Power Off.

The one that's not a perfectly round.