Comment #25 on issue 2307 by [email protected]: as_coeff_mul()[0] != as_coeff_Mul()[0] when the coeff is Number (not Rational)
http://code.google.com/p/sympy/issues/detail?id=2307

Another important difference between the two methods is that as_coeff_foo allows you to define what goes into the coeff by using the deps whereas as_coeff_Foo only pulls out a Number. If you want to put distance between the names consider the latter to be called as_Num_Mul().
    >>> (3*x*y*z).as_coeff_mul(y)
    (3*x*z, (y,))

Both methods are like specialized calls to as_independent.

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