The current rating of a fuse represents the minimum sustained current the fuse will blow at ... eventually. A 1A fuse will take 1A for a very long time without blowing, and if the fuse can dump some heat into the PCB or has airflow across it, may never blow at 1A.

The critical parameter is the \$I^2 \cdot t\$ rating, which gives you an idea of the energy (power and time) needed to blow it. (Remember that fuses are really meant to protect circuits when there are catastrophic failures.)

It's crucially important to match \$I^2 \cdot t\$ ratings, since if you replace a fast acting fuse with a slow-blow type, even thought they both say 1A, it's going to take radically different energy levels to actually blow them.

When the fuse is intact, you only have an \$I \cdot R\$ voltage drop across it. This drop is going to be nowhere close to the voltage rating of the fuse (else it acts like a big resistor and limits the energy available to your circuit.) Once the fuse blows, the voltage rating comes into play, which represents how much voltage potential the open fuse can withstand without flashing over and re-energizing the compromised load circuit.

4:40am
Rushing.

If you search prior material on Stack Exchange EE you'll find a substantial amount of material on this.
The figures you cite are in the order of right.
Fuse blowing current and fault clearing current are different.
HRC (high rupture capacity) fuses exist to deal with this difference. The ceramic bodied fuses you see in better equipment are HRC.
A glass fuse may blow but sustain an arc of 100's of amps long enough to kill you.

If your pole fuse is 100A and your neighbours is 100A and ... what is the street cct able to supply?

If you draw 50A from your home mains supply and it sags 1%, what current would you expect it to supply if you hard shorted it?

At 50 Hz, 230 VAC, what inductance do you need to add say 1 Ohm reactance to your house feeder circuit. What inductance do you think the feeder has?

A friend had an electrician (stupidly) reverse phase and neutral when wiring up their house.
Steam came out of the cold taps due to electrical heating in the grounded copper "cold" water pipes as current flowed from mains phase via switchboard ground to copper pipes and thence to ground. (really)
and worms crawled out of the ground (really)
and they tell me that the house made groaning sounds.
I imagine that that was probably from water boiling in the cold water pipes.
What current do you think flowed :-) :-( ?

HRC fuses - there will be somje ueful links there.

Wikipedia - fuses

• The breaking capacity is the maximum current that can safely be interrupted by the fuse. Generally, this should be higher than the prospective short circuit current. Miniature fuses may have an interrupting rating only 10 times their rated current.
  Some fuses are designated High Rupture Capacity (HRC) and are usually filled with sand or a similar material. Fuses for small, low-voltage, usually residential, wiring systems are commonly rated, in North American practice, to interrupt 10,000 amperes.

Wikipedia - breaking capacity

• Miniature circuit breakers and fuses may be rated to interrupt as little as 75 amperes and are intended for supplementary protection of equipment, not the primary protection of a building wiring system. In North American practice, approved general-purpose low-voltage fuses must interrupt at least 10,000 amperes and certain types useful for large commercial and industrial low-voltage distribution systems are rated to safely interrupt 200,000 amperes..

ADDED

Stack Exchange:

Similar material.

Fuses: What are the practical differences between Ceramic and Glass cartridge fuses

What is the Thévenin equivalent of the mains power supply? - 1st approximation - a piece of copper busbar :-)

The Impact of Mains Impedance on Power Quality

Useful. See fig 6.
Note transformer impedances specified as a % - this is the % drop in output voltage at rated load.

Added 2:

Thanks for the clarification of breaking capacity and highlighting reactance. I still think 2000 amps is over the top. 200 amps I could understand.

I'd guesstimate that 2000A would probably be getting on the high side in a residential situation. But 200A is far too low.
Far far too low.

If you can get 50A intended current at your home's distribution board and your neighbour's lights do not flicker, what would you get if you shorted it?

People have died from mains arc discharge that was improperly interrupted.

Standards typically allow a 5% V drop at the farthest outlet from the distribution board in a home at rated load.
At 20A rate that implies available current is ~+ 20A/0.05 = 400A.
And that's worst case on house wiring!.