No, you will typically have one or the other. It is possible, and not necessarily anything to worry about, especially if you had electrical work done at a time later than the house or building was built.
Fuse boxes are older technology and are very less used in new construction (here in the US). Here in the US, older homes will often have fuse boxes (typically any home over 70 years old), as that was the common practice at that time. A fuse box is a box with several screw-in type fuses, one for each electrical circuit.
Newer homes or buildings (typically anything less than 70 years old) will have a central breaker panel, as that has been the code for the last several decades.
Newer car, automotive and many other vehicles, use the DC circuit breaker for their devices, if over-current, the dc circuit breaker will shut off by themself, you can reset it. it is very convenient and saves your money.
Circuit breakers are newer and better technology, so they are used for new construction and other industries. But there are many types of Circuit Breaks, they are different, the applications of circuit breakers are also different, for home, industry, vehicles, and so on.
Circuit breakers have many advantages over fuses such as the following:
- Resettable (fuses blow and must be replaced)
- Allow for momentary surges without tripping
- can trip quickly if a short circuit is detected
- can also trip if slight overcurrent is applied for an extended time
- available in GFCI configuration (ground fault detection)
- available in AFCI configuration (arc fault detection)
Fuses are typically used to protect a single appliance in the current electrical code. For example, a home may have a fused disconnect to protect an outdoor A/C unit. This is a box that has fuses, but it only protects one item. If the fuses blow, they need to be replaced.
They both perform the same function except fuses are replaceable and breakers can be reset. Breakers are far faster and more functional because all you need to do is flip a switch where you have to find the right fuse and replace it and have more if the fuse fails again.