Fuses are designed to protect the cable and electrical delivery system and not the machine or the user. The fuse is there to stop too much current being drawn which will cause a cable that is too thin to heat up and possible catch fire. Current is best thought of as the amount of water flowing in a stream, voltage is the speed at which it flows. The cable is the banks of the stream, too much water, it overflows.
Power or heat as it becomes, is calculated by current * current * resistance of the wire. So, the lower the resistance of the wire the better. For each thickness of wire, there will be stated maximum current carrying capacity.
When a motor starts up, the arrangement inside the motor results in close to a short circuit. Once the motor starts moving this short circuit no longer exists. When switching on a motor you have what's called the surge current, this is the peak current that is ever drawn by the motor and normally only last a second or two as the motor gets going. A normally household fuse is a 'B' class, which means that if it sees a high current it reacts to stop the supply quickly. The surge current will be much higher than any fuse you would ever put into the circuit. So, to get around the surge current you need to use a fuse that reacts to a big current at a slower rate. This is a C class circuit breaker. If you connect a 16A or a 32A circuit breaker to a machine, that are ba rated it is likely that they will trip when you switch the machine on. You may also get away with it. This is a safe situation. No problem. However, if they trip you need to use a ca class rated fuse.
Never, and I mean never use a device, wire, plug, socket rated at a lower current than the circuit breaker or fuse that is protecting the circuit. Ie. It's safe to use a 32A plug and socket on a 16A breaker but not a 13 A plug.
The main reason for this is that in a fault, the short circuit will potentially cause the under rated item to over heat and catch fire. When using a saw for instance, most of us have at some point stalled the motor on a small circular saw. You have created a short circuit and a big current is rushing down the wire as a consequence. The last time I did it, the motor of the machine I was using caught fire! Exciting! I always have a fire extinguisher close to hand luckily.