Modern electrical systems have enormous capacities for destruction when short circuits occur. Proper fusing is critical. One cycle of high fault current can vaporize wiring and insulation, warp bus bars, and blow up fuses. To prevent such catastrophes, you need to know four key characteristics: voltage, amperage, interrupt capacity, and current-limiting ability.
The voltage rating must match or exceed the voltage of the circuit. Generally, fuse sizes prevent serious mismatches. For example, most 250V fuses are smaller than most 600V fuses. Thus, the larger fuses won't fit in the smaller fuse clips. However, some will (like fuses you use in industrial control circuits).
The amperage rating or current-carrying capacity must match the full-load current of the circuit as closely as possible. Undersized fuses blow easily. Oversized fuses may not provide enough protection. You can install fuses of different amperage ratings in the same fuse clips. For example, you can swap one manufacturer's 600V fuses in the 35A to 60A range. Those fuses are physically, but not electrically, interchangeable. The same is true of fuses in the 70A to 100A range. However, you can't use the 35A to 60A fuses in place of the 70A to 100A fuses.
Interrupt capacity is the total current the fuse can interrupt without damage. Many fuses have interrupt capacities as high as 200,000A, because many industrial facilities have available fault currents that high. Other common interrupt ratings are 10,000A, 50,000A, and 100,000A.
Current-limiting ability is a measure of how much current the protective device will "let through" the system. Even a single cycle of 200,000A current will severely damage any installation. Current-limiting fuses respond much faster when currents are high. The current-limiting ability of the fuse is expressed as a number, such as "K1" or "K5." K1 is more current-limiting than K5.
Replacement fuses should be identical in all respects. If an identical replacement is unavailable, you can use a fuse with a higher amp rating. However, you should replace it with one of the proper size as soon as possible. You will, in the meantime, have a system that compromises protection for components; or may not protect them sufficiently to prevent destruction. You can use a fuse with a lower amp rating, but it is likely to blow.
When substituting fuses, never reduce the voltage rating, interrupt capacity, or current-limiting ability. Serious damage to property and serious injuries may result.