Live: This is a bootable image that can be run from the USB stick (or DVD).

NetInstaller: This is the same installation program as the full installer, but the downloaded image includes only enough to get the computer booted and connected to the Internet, and the rest of the packages are downloaded as needed during installation.

The installation image includes the complete Kali system, so it can be installed without having an Internet connection. The basic 'Installer' is text-only, and the 'Graphic Installer' is the same thing with mouse support added (but still no other graphics or GUI). But the important thing is that it does the job very, very well in almost every situation and on almost every kind of system, without having to worry about graphic adapters, display resolution or much of anything else. It is a very old installer, primarily text-based, with no spiffy GUI interface. Yes, I can hear a lot of users out there going 'Ugh'.

Full Installer: This is a slightly modified version of the Debian GNU/Linux installer.

32-bit (i386) and 64-bit (amd64) versions: Some distributions have dropped 32-bit support, but not Kali.

The installation images available on the Kali Downloads page are:

So I am going to run down some of the possibilities, in hopes of clearing it up a bit. Kali is available for installation in a number of different formats, for a number of different systems, and that variety can sometimes be a bit intimidating.

Download kali linux for vmware