The answer to 'types of fuse box' is that there are several common types of fuse boxes used in homes. The most common are the circuit breaker panel and the older style fuse box. Circuit breaker panels contain individual circuit breakers that can be reset if a circuit is overloaded, while fuse boxes use replaceable fuses that need to be swapped out when a circuit is overloaded.
Fuse boxes are less common in modern homes, but they are still found in older buildings. They typically have a series of fuse slots that hold the individual fuses for each circuit. When a circuit is overloaded, the fuse will 'blow' and need to be replaced with a new fuse of the correct amperage rating.