We compare the continuous and discrete truncated Wigner approximations of various spin models dynamics to exact analytical and numerical solutions. We account for all components of spin-spin correlations on equal footing, facilitated by a recently introduced geometric correlation matrix visualization technique [R. Mukherjee {em et al.}, Phys. Rev. A {bf 97}, 043606 (2018)]. We find that at modestly short times, the dominant error in both approximations is to substantially suppress spin correlations along one direction.