Yes pickled cabbage is the same as sauerkraut because to make sauerkraut you have to pickle cabbage so it's the same thing.
Sauerkraut is made from cabbage that has been pickled and fermented.
To make Sauerkraut the cabbage is shredded, salted and left to ferment in a de-oxygenated environment for 4-6 weeks.
Salt pulls water out of the cabbage via osmosis when then forms a brine that helps protect the sauerkraut during the fermenting process.
So in short yes Sauerkraut and Pickled Cabbage are the same thing.