Difference between constant speed and variable pitch propellers?
Your understanding is essentially correct.  A constant speed prop is governed.  A variable pitch prop is not.

Constant speed props are also variable pitch.

A constant speed prop will only maintain speed if there is sufficient power from the powerplant.

Most constant speed props will require slight tweaking to maintain the rotational speed during a flight.

Constant speed props require a governor, and the flyweights are a component of a governor.