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It's the same as a fuse box. Sort of. The electric service panel used to be called the fuse box, fuse panel,  circuit breaker panel, or any number of other terms. Today, most homes have what we call the electrical service panel, or simply, the service panel. It's not literally the same thing, but it does provide the same function.
There are a lot of names that refer to the power supply unit for your electric fence system. I have seen or heard them referred to as: energizer, energiser, charger, fencer, shockers, zappers and many other names. These are all names referring to the energy source used to deliver energy to electric fences. They come in all shapes, sizes, colors and performance ratings. For this article I will use the term energizer since I feel that name is the most self-explanatory.