Isomorphism questions for metric ultraproducts of finite quasisimple groups

New results on metric ultraproducts of finite simple groups are established. We show that the isomorphism type of a simple metric ultraproduct of groups $X_{n_i}(q)$ ($i\in I$) for $X\in{{\rm PGL},{\rm PSp},{\rm PGO}^{(\varepsilon)},{\rm PGU}}$($\varepsilon=\pm$)alonganultrafilter$$\mathcal{U}$$ontheindexset$I$forwhich$n_i\to_{$\mathcal{U}$}\infty$determinesthetype$X$andthefieldsize$q$ up to the possible isomorphism of a metric ultraproduct of groups ${\mathrm{P}\mathrm{S}\mathrm{p}}_{n_i}(q)$ and a metric ultraproduct of groups ${\mathrm{P}\mathrm{G}\mathrm{O}}_{n_i}^{(\epsilon )}(q)$. This extends results of Thom and Wilson.