Thermobaric explosives include FAE bombs, but strictly speaking are different in the way they detonate. The FAE has a faster explosive rate due to the type of fuel and position of the detonator. Big bang - fast bang. Good for daisy-cutters which was the way they were used by the US, say, in Vietnam for clearing jungle canopy.
What is now referred to usually as "thermobaric" is a weapon pioneered by the Russians that uses a type of powdered filler that explodes slower and expands through the atmosphere as it burns. The result is a cavity filling slow-burn explosion that heats the atmosphere beyond the temps needed for self-explosion of the bomb's filler. The overpressures created by this weapon are the same as a nuclear detonation. If used in caves, to use the most current examples in Afghanistan, the explosion doesn't burn out almost immediately, but instead follows the oxygen source all through the tunnel system, expanding and feeding on itself, extinguishing when the oxygen is consumed - not when the filler is consumed. Much more destructive weapon than an FAE.
Sorry to lecture, but it's a common misunderstanding. The thing that makes the weapon usable in a grenade round (the Soviets developed RPG loads with them for bunker busting) is that the "thermobaric" filler is a solid metal powder that scatters when the casing explodes and doesn't require the time to spray its' contents like a liquid filled FAE does. Just shoot/drop it and it goes off and expands from there. FAE's spray the filler in mist for a short time (the bigger the bomb, the longer the time), then the detonator goes off inside the cloud. The MOAB is an example - good videos are around showing it do that.
A thermobaric is fiendishly simpler and amazingly more efficient and the terms used to describe it vs. FAE get muddled a lot.
