Live - Live boot, as ususal.
Live (failsafe) - boots with a minimal set of drivers and hardware checks.
Live (forensics) - Boots without mounting anything, suitable for forensics work.
Live USB Persistence (and encrypted) - Just add needed partitions, and boot menu is ready for persistence.
Install - Regular, text mode installation.
Install Graphical - GUI installation mode.
Install with speech synthesis - Kali installation for visually impaired users.
Hardware Detection Tool - designed to display loe-level hardware information.
Memory Diagnostic - erm, diagnoses memory?
Note: The above informatin derive from Kali Training