REX , originally created by Rebug Team, is a conversion of CEX & DEX firmware.
PEXis the same, being a CEX & DEX conversion (by @evilnat), with PEX having one difference in it uses a DEX firmware from 4.84 (final release) and ports the needed modules to current CEX Firmware, since there is no longer DEX firmware's released for the PS3.
Cobra CFW
Cobra CFW is a community created CFW type
The Firmware contains a payload (formerly CobraUSB product) in the CFW that provides additional features and functions. From v6.0+ to current v8.5 Cobra has been maintained and expanded on by an open community of developer's since its payload went open source.
noBT / noBD CFW
This is a CFW that targets broken console's that otherwise would not work, (See more info)
DualBoot FW
A community created small modification to Official firmware
The idea, you could go from CFW to OFW without re-exploiting flash to re-install a CFW
Useful for user's who did not want have an active modded console in game servers and risk a ban.
You must already be on CFW to use this type of firmware.
(Concept originally by @Habib)
HFW
A community created small modification to Official firmware
OFW firmware 4.83 patched the webkit used in 4.82 OFW, HFW simply swaps out the patched webkit (in 4.83 +) with the unpatched webkit from 4.82.
The 4.83 patch was PlayStation last attempt to patch any jailbreaking exploits
