Xcorr versus Correlation through toeplitz matrix

Hi all I am working on correlations and came across a query. If we calculate xcorr of M signals of length N each, we get an output matrix of size (2N-1)xM^2. however, if we do the same through Toeplitz Matrix of size (2N-1)x2M^2, we get an output matrix of size 2M^2 x 2M^2. I am confused as to how the elements of both ways can be equalized? Correlation is a special form of convolution, though it is not distributive and commutative. But what I am doing, I suppose, does not relate to this. Any help in this will be appreciated. Cheers Sal