Difference between various numpy random functions

Nothing.

They're just aliases to random_sample:

In [660]: np.random.random
Out[660]: <function random_sample>

In [661]: np.random.ranf
Out[661]: <function random_sample>

In [662]: np.random.sample
Out[662]: <function random_sample>

In [663]: np.random.random_sample is np.random.random
Out[663]: True

In [664]: np.random.random_sample is np.random.ranf
Out[664]: True

In [665]: np.random.random_sample is np.random.sample
Out[665]: True