If A is an n x n matrix and B is n x m, solving A\B is tantamount to solving m*n equations in m*n unknowns. Finding the inverse of A is equivalent to finding A\eye(n), and hence is similar to solving n*n equations in n*n unknowns. If the number of columns, m, in B is less than n, it therefore takes less time to solve m*n equations than doing inv(A)*B which would involve n*n equations combined with a matrix multiplication.
If A is n x p and not square with p < n, solving A\B requires solving m*n equations with only m*p unknowns and is overdetermined, so A\B will simply find the best least squares approximation to a solution, which makes it different from 'inv' which will produce an error.
On the other hand if p > n the number of unknowns exceeds the number of equations and the system is underdetermined. Hence A\B will assign some of the unknowns arbitrary values. In this it also differs from the 'inv' function which will again give an error.