The 386 was the first CPU that could do real protected mode and could run in 32 bit mode. The 286 could switch to protected mode as well but not back to real modus without resetting the processor. It's successor can switch back without a reset. This allowed the programmers to create programs that could use the protected mode.
Because the 386 was fully 32 bits it was very expensive. This lead to the creation of the 386SX (the normal 386 was called DX) which was 32 bits internally but had a 16 bits bus. Practically the same story as with the 8086 and 8088 which was 16 bit internally and had a external 16 bits and 8 bits bus respectively. Also don't confuse the SX/DX-story of the 386 with the 486. Both the 486SX and DX were fully 32 bit but the SX part lacked a maths co-processor. If you wanted a co-processor for your 386 you had to buy an additional 387 processor and install it along with your 386DX or 386SX.
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