My question is whether "politisch korrekt" conveys the same meaning as "politically correct" does in English or is there another term that describes this better?
It's exactly the same meaning and usage. In fact, the words have been translated literally, the meaning imported into German from English. I don't know about the English connotation, but in German, it can have a negative connotation. It tends to complicate language by forcing statements to be gender-neutral and non-offensive to societal minorities.
Taken to its extreme, the negative connotation of PC is considered by some as a form of censorship by dodging the issue through noting a lack of PC in a statement. "Politically Incorrect" is the (probably ironic) name of a German blog that, depending on your view, spreads "forbidden" or "suppressed" (i.e. politically incorrect) news and views and as such is a herald of freedom; or it spouts hate speech against foreigners, muslims, jews, and other old and new targets of the extreme right/Neo-Nazi scene.
Depending on what you try to express with pc, whether it is more or less opportunistic, cowardly, streamlined, diplomatic or what else. Most often politically correct is used nowadays, but of course it isn't a new phenomen, and was observed in former times. 20 years ago, it wasn't used in Germany, afaik, but instead more specific terms were used, depending on the context and what should be expressed:
- ein Fähnchen im Wind
- ein Wendehals
Note, that the expression is almost always used, to describe somebody else. It will be hard to find anybody, who describes himself as pc.
Germans do not need their own word for that - For the rare cases were we use it, the English term works quite well. Political correctness plays (maybe apart from politics itself) a much smaller role in German society than it does, for example, in the United States. Most people don't care beyond simply "behaving".
And no, the direct translation does in my opinion not (maybe, not yet) transport the same notation as the English term in German. "Politisch" refers to politics in German - nothing else. "Angepasste Sprache" or the original English term tends to work better in most cases.
Although this discussion does not belong here, it is hard to resist to challenge that changing language by kind of disapproving of certain terms could possibly change mindsets. Someone who thinks "cripple" will most probably not start to think different if you tell him to use "handycapped".