ATI
The company was founded by Kwok Yuen Ho in 1985 as Array Technology Inc. and later known for their Radeon graphics cards. The first few graphics cards brand, the ATI Wonder series and ATI Mach series, were released in 1986 and 1990 respectively. In 1995 they released the ATI Rage graphics cards series and later in 2000, they released the ATI Radeon (now known as AMD Radeon since 2010). It is also the rival to Intel and Nvidia in the GPU market.
On July 24, 2006, AMD acquired ATI with value about 5.6 billion USD, and since then some AMD CPUs contains a ATI Radeon graphics core. In 2010, AMD abandoned the ATI brand for graphics products, in favor of the AMD name.
Radeon - ATI's (now AMD) graphics products for gamer
FirePro - Formerly FireGL, it is ATI's (now AMD) graphics products for workstation
AMD - The company who acquired ATI
Nvidia - ATI's rival in the GPU market (and later, AMD's rival after the acquisition)
ATI (Japanese)