Just to add a little more info than Blix provided.
ICR batteries are Lithium Ion batteries that use a more volatile chemistry, and require protected circuits in case they are pushed enough to short. This is why they are a little longer than IMR batteries; the protective circuits add a little length to the battery. Even with the built-in protection, it might still be a good idea to use the 2 cent or Vape Safe protective circuit
Batteries : Vape Safe Mod Fuse 2.
IMR are high drain batteries that V-V and V-W APV's generally require for their voltage boost circuits; they also use a safer, less volatile chemistry.
AW batteries are not really a "brand" that is manufactured by a single company. There's a guy in China who purchases large quantities of batteries from several manufacturers; he tests and examines them by hand and then "re-brands" the best ones as AW.
I use IMR batteries in both my V-V and mech mods. I've used only AW's for several months, but I did recently purchase some Efests recently just to try a different brand out. Both have good reputations among the battery experts, as do Panasonic and Sanyo.
I don't trust any battery that has "fire" in the name. And I would not trust a "no name" battery.
