In a general nutshell:
Protected batteries (IRC) have a protective circuit built in to "help" avoid a short or other battery catastrophe. They will often have higher mah ratings compared to an IMR. The mah stands for something like mili amps per hour (not sure). 100 mah is equal to 1 hour battery useage. So an 2000 mah battery should last 20 hours of use on average. These are often used in mechanical mods.
Unprotected high drain, or IMR, batteries are made with a safer chemistry. They are naturally not as liable to short out and therefore do not require protection. These are most often used in variable voltage devices which utilize a boost circuit to provide high amps of power in brief moments. All variable voltage mods have inborn protection in their circuitry.
I'm not familiar with the other category of battery that you inquired about, or I just do not recognize the abreviation.
Most mods are very particular about the length of the battery, and also how the top of the battery makes contact: flat top or nipple/button top.