BIOS and UEFI
UEFI was introduced with Windows 8 as a replacement / upgrade to the BIOS system. One example of this upgrade is that it allows for computers to use hard-disks larger than 2 Terabytes (2,000 Gigabytes). Unfortunately, UEFI was also secretly manipulated by Microsoft in tandem with certain hardware manufacturers to prevent - or at least make it very difficult - to replace or dual boot Windows 8 with another operating system.
Unified Extensible Firmware Interface (UEFI)
The GRUB is used to manage and boot up linux operating systems on computers that use the BIOS system. These are typically older computers or those that did not come with Windows 8 pre-installed. It is worthwhile noting that the UEFI can be disabled on many systems to run using the BIOS instead; this is known as running in Legacy Mode. Computers sold prior to the release and pre-installation of Windows 8 - which introduced UEFI - will therefore use the BIOS.