libjpeg is a library written entirely in C which contains a widely-used implementation of a JPEG decoder, JPEG encoder and other JPEG utilities. This library is maintained by the Independent JPEG Group.
libjpeg-turbo is a high-speed version of libjpeg for x86 and x86-64 processors which uses SIMD instructions (MMX, SSE2, etc.) to accelerate baseline JPEG compression and decompression. libjpeg-turbo is generally 2-4x as fast as the unmodified version of libjpeg, all else being equal(for non-grayscale JPEG compression and decompression, libjpeg-turbo is between 1.8x and 4.5x as fast as libjpeg v6b).
libjpeg-turbo was originally based on libjpeg/SIMD by Miyasaka Masaru, but the TigerVNC and VirtualGL projects made numerous enhancements to the codec, including improved support for Mac OS X, 64-bit support, support for 32-bit and big endian pixel formats (RGBA, ABGR, etc.), accelerated Huffman encoding/decoding, and various bug fixes. The goal was to produce a fully open source codec that could replace the partially closed source TurboJPEG/IPP codec used by VirtualGL and TurboVNC. libjpeg-turbo generally achieves 80-120% of the performance of TurboJPEG/IPP. It is faster in some areas but slower in others(for non-grayscale JPEG compression and decompression, libjpeg-turbo 64-bit is between 80% and 118% as fast as TurboJPEG/IPP. libjpeg-turbo 32-bit is between 60% and 93% as fast as TurboJPEG/IPP. libjpeg-turbo‘s primary weakness relative to TurboJPEG/IPP is 32-bit performance, particularly on Intel processors and even more particularly on legacy Intel processors. This is largely due to the Huffman encoder/decoder running out of registers and having to swap some inner loop variables back and forth from memory).
In one word, libjpeg-turbo is a fork of libjpeg that uses SIMD instructions to accelerate JPEG encoding and decoding.
btw, projects such as Mozilla and fedora switched to libjpeg-turbo in 2010.