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pyplot is a module in Matplotlib; and PyLab is a module that gets installed alongside Matplotlib. PyLab is a convenience module that bulk imports matplotlib. pyplot (for plotting) and NumPy (for Mathematics and working with arrays) in a single name space. Although many examples use PyLab, it is no longer recommended.
Since heavily importing into the global namespace may result in unexpected behavior, the use of pylab is strongly discouraged.
Pylab is a module that provides a Matlab like namespace by importing functions from the modules Numpy and Matplotlib. Numpy provides efficient numerical vector calculations based on underlying Fortran and C binary libraries. Matplotlib contains functions to create visualizations of data.
The matplotlib. pyplot is a collection of functions that make matplotlib work like MATLAB. Each pyplot function makes some change to a figure: e.g., creates a figure, creates a plotting area in a figure, plots some lines in a plotting area, decorates the plot with labels, etc.
This wording is no longer in the documentation.
Use of the pylab import is now discouraged and the OO interface is recommended for most non-interactive usage.
From the documentation, the emphasis is mine:
Matplotlib is the whole package; pylab is a module in matplotlib that gets installed alongside matplotlib; and matplotlib.pyplot is a module in matplotlib.
Pyplot provides the state-machine interface to the underlying plotting library in matplotlib. This means that figures and axes are implicitly and automatically created to achieve the desired plot. For example, calling plot from pyplot will automatically create the necessary figure and axes to achieve the desired plot. Setting a title will then automatically set that title to the current axes object:
Pylab combines the pyplot functionality (for plotting) with the numpy functionality (for mathematics and for working with arrays) in a single namespace, making that namespace (or environment) even more MATLAB-like. For example, one can call the sin and cos functions just like you could in MATLAB, as well as having all the features of pyplot.
The pyplot interface is generally preferred for non-interactive plotting (i.e., scripting). The pylab interface is convenient for interactive calculations and plotting, as it minimizes typing. Note that this is what you get if you use the ipython shell with the -pylab option, which imports everything from pylab and makes plotting fully interactive.
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