Yes, both the red and black Trustfire and the AW IMR will fit in the REO mini. The Trustfires are protected LiIon
batteries. The IMR
batteries use a different chemical makeup to store the charge. They are considered "safe chemistry" batteries and do not need a protection circuit.
IMR batteries are also called high current drain batteries, meaning that they can keep up with an electronic circuit that draws a lot of current. This comes into play when using 1.5 ohm atomizers at 3.7v. With IMR's there's a more consistent vape throughout the battery's charge, whereas LiIons will taper off more in the middle and end of the charge.