The explanation is a bit awkward because I'm trying to describe numerous situations. (pre-2.2 kernels, post-meldown kernels, in-between kernels, 32-bit builds, 64-bit builds, using PCID hardware, not using PCID hardware...) It looks like 7 of the 12 possibilities are valid, more or less.
Some segment registers are reloaded on a 64-bit system. That includes CS, DS, SS, and GS. The 32-bit systems must additionally reload ES. All segment registers are loaded for Linux 2.0 and older, via hardware task switching.
CR3 does not get written for system calls when running on a normal Linux from version 2.2 until the meltdown workaround hit.