Numpy, scipy, matplotlib, and pylab are common terms among they who use python for scientific computation.
I just learn a bit about pylab, and I got confused. Whenev
No, pylab is part of matplotlib (in matplotlib.pylab) and tries to give you a MatLab like environment. matplotlib has a number of dependencies, among them numpy which it imports under the common alias np. scipy is not a dependency of matplotlib.
If you run ipython --pylab an automatic import will put all symbols from matplotlib.pylab into global scope. Like you wrote numpy gets imported under the np alias. Symbols from matplotlib are available under the mpl alias.