This isn't the case, at least for UK English. The phrases can mean the same. "Stop taking the piss" and "Stop taking the piss out of him" have the same basic meaning, if you want someone to stop mocking someone. A (UK) alternative is to "take the mickey". (Wikipedia is wrong about this.)
Yes, it can also mean this - but I wanted the Russian for the first use.
NB It can also be used (in UK, not colonial, English (joke, Robert)) when someone is going too far. You agree to babysit for some friends and they say they'll be back at ten but turn up at 2 am - you can quite reasonably say "You're both taking the piss!"
Thanks for the Russian suggestions!