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Correlating random numbers seems to skew the data

First off, apologies for the cross-post from mathematics, but I found this site later and think it would be a better fit for the question (besides, there has been no comments/answers on mathematics ...
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Does one use the covariance or correlation matrix in cholesky decomposition to generate correlated samples

Can we interchangeably use Cholesky decomposition of covariance and correlation matrix to generate simulations? If not, in which situations do we use one or the other and why? Thanks in advance.