"fixed" and "X" are equivalent, requesting the fixed effect design matrix.
"random" and "Z" are equivalent, requesting the random effect design matrix. Note that this is an equivalent version of the design matrices such that the tcrossprod will be the contribution to the marginal variance-covariance. This is not necessarily the one computed directly from the random argument passed to varComp. These are actually computed from cholRoot of \(\mathbf{K}\) matrices.
"varcov" and "K" are equivalent, requesting the contribution of each random effect to the marginal correlation matrix. These are not necessarily the same value passed to the varcov argument of varComp, because the input value will be treated as the "\(G\)" matrices when random is not missing, but the result here will always be "\(\mathbf{K}\)" matrices. See varComp for notations.