How to remove caps on circular faucet handles?
You're correct, its similar to the shower control.

You need to unscrew the cap anti-clockwise.
There is a good chance that there is a decades worth of crud jamming the cap.  You could trying pouring hot water (from a kettle) over.  this may dissolve some crud, and may also loosen it by expansion.
You could try using a "jar-opening" gripper, to ensure you have a really good grip.
Alternatively, try wrapping cello-tape around the knob as protection, then CAREFULLY using multi-grip pliers.