Yes the voltage is the critical value, that has to be correct for the camera (or other electronic) system to function correctly. The mAh rating is a rating of how much energy the battery can store, and then supply, in other words the capacity (not capacitance, that's something else entirely). Effectively a 2600mAh battery can supply 2600mA (or 2.6A) for one hour, while an 1865 mAh battery can only supply 1865mA for one hour. Of course usually the electronics is drawing much less than the rated load, so if the camera only draws 500mA that means the 2600mAh battery should last for 5hr 12min, while the 1865mAh will only deliver for 3hr 43min 48s. Well theoretically, it won't be that accurate in real life, but you get the idea. It allows you to work out how long something will last given the working current draw.
I am currently working on the control systems for some 12 volt powered clay pigeon traps, mounted on a trailer. The total current draw for the system, when everything is running is 63A, so we have to install a 120Ah sealed lead acid leisure battery to provide a decent run time, normally we would use a 60Ah battery for a single trap, running at around a max load of 24A, which would give nearly three hours of continuous use. The total load in the trailer means that we have to use some really heavy duty cable to run from the battery to the control panel, just to stop it overheating. The smaller cables might happily run at 85C, but the customer won't be very happy if they touch one and get burned, so we have to use a much higher rated cable to keep the temps down. The joys and worries of designing stuff
. At least testing the systems out is a good excuse to get out the shotgun and do some shooting.
Alan