The 80386 chip has one big advantage over the 80286: it includes fully functional, built-in circuits for multi-tasking, or running two or more programs at the same time. Although software like Windows, DesQview, or Unix will let you "multi-task" using lowlier chips, the 80386 does it more reliably and with less hassle. Windows, for example, running in "386 Enhanced Mode," lets you use multiple standard DOS programs at the same time, whereas you're limited to only one DOS program at a time with an 80286. Another improvement in the 80386 is its ability to access even larger amounts of memory than the 80286, and to do so with less trouble. Again, DOS is oblivious to the extra memory, but you can buy software that bypasses this limitation through a DOS extender.
The 80386 comes in two versions: the standard model, called the ox, and the cheaper, slightly slower SX. The only difference is that the DX accesses data 32 bits at a time (it has a 32-bit bus), while the sx can only move 16 bits at once. That makes a PC based on the 386DXsomewhat faster than a PC that uses a 386sx- but nowhere near twice as fast, since both chips do everything else with equal speed.