Can I replace a battery with a source of the same voltage but different capacity (mAh)?
The mAh rating of a battery is two-fold generally. 

First it tells you something about its capacity (at full state of charge). The product of Current and Time is definitively Charge (as in Coulombs). Using a lower rated mAh battery pack will most likely just mean its battery life is shorter.

Second, for rechargeable batteries, it tells you something about the safe rate at which the battery can be charged, often stated in C's. So a 1400 mAh battery might ideally be charged at 1.4A maximum. This is just a rule of thumb type of thing, certainly refer to your battery manufacturer's data sheet for definitive information on this. But if you are replacing a 1400mAh battery with a 700mAh battery, I would be really careful about using the same charging system with a lower mAh battery pack.