If a runner scores on a wild pitch, it's the pitcher's own fault and he is charged with an earned run; but, the catcher is beyond his control and the run is unearned. All correct?
I think you left out a word or two, but yes -- WP, pitchher's fault, earned run; PB, catcher's fault, unearned run.
All of this assumes that no hit ensues that would have scored the run anyway.
The same is true if a runner advances to a base from which a hit would not have scored him without the WP/PB; also correct?
scroll down to 10.16
For example, with two outs, a runner on third base scores on a passed ball. For the time being, the run is unearned since the runner should still be at third. If the batter strikes out to end the inning, it will stay that way. If the batter gets a base hit, which would have scored the runner anyway, the run now becomes earned.