Olesya,
A pipe nipple is simply a short piece of pipe generally limited to a length up to 12". Common lengths are 3", 6", and close nipples (short, fully threaded). You can specify whichever length you desire. A pipe nipple is still a pipe nipple regardless of it's end condition.
POE, TOE, PBE, TBE are all just end the conditions. They stand for Plain One End, Thread One End, Plain Both Ends, Thread Both Ends. This does not have an impact on the length.