I thought about this one a lot, and I I'm not a hundred percent sure myself. I think I'd have to get the OED definition for a really comprehensive answer. I did realize something that I hope helps, though. From use, I would say charge is typically used in situations that involve something non-countable (like charging a battery) and load is used in situations that involve something which is countable (load a cannon). I've seen both words used as nouns, and I'm sure there are probably exceptions (especially with archaic use). Countable for load and non-countable for charge should keep you safe for general use most of the time, though.

They are quite different. 'Charge' as a verb, means a number of different things, but in relation to 'load', it means to restore power to a battery - to 'load' power. 'Load' simply means to fill something - load a truck, load something onto the truck, load a gun with ammunition.