The 80386SX is a "lite" version of the 80386DX chip. It uses only a 16-bit data bus, the same external bus width as the 80286. It also only can address 16 MB of memory, like the 80286. The SX version of the 386 chip was in fact released well after the DX, and in some ways was intended to move the market away from the 286 since it had roughly the same interfaces but better performance. It was actually introduced several years after the DX.
It is a common myth that the 80386SX can be substituted in place of an 80286 in a 286 motherboard. While the chips are compatible in terms of their external interfaces they use different packaging. A 386SX could be put into a 286 motherboard if a proper adapter were used.
The narrower data bus width of the 386SX creates a reduction in performance of about 20-25% compared to an equivalent-speed 386DX; a significant difference but not excessive.
The 80386SX chip was a popular choice for the first small notebook computers, especially the 386SL variant that introduced the SMM power management features to the Intel line. The 386SX is still a 32-bit processor internally and will run 32-bit software (really slowly :^) ). It is available in speeds from 16 to 33 MHz; a 40 MHz version was not produced for the SX, and is also available in cloned versions from AMD and Cyrix.
The 386SX chip is today considered obsolete.