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I have a four way switch in the house (I assume that is the correct term, 4 switches all controling the same light; flipping any one of them toggles the light; no other lights are affected).

I am looking at the wiring diagram (this is an EU one for Belgium) and I see the following symbol for one of the switches:

But other switches have this symbol:

It would seem to me that on an n-way circuit all of the switches would have the same symbol since they all connected to the same number of other switches.

Is this true? Or is there something I don't understand?

If all the switches are the same, on the schematic (that is, the diagram not relating to the physical location of the switches, but just what is on each circuit), is it necessary to repeat the symbol or can you just write "x4"?

Note - these remarks are from a North American perspective, but I believe switching is done the same way in Europe.

Switch terminology can be confusing but once you understand it, it is pretty simple.

When there's just one switch controlling the lights, it's simple, just a plain switch, labelled ON in the up position, OFF in the down position. Technically this plain switch is a single pole single throw (SPST) switch but that's not important, nobody uses that term for building wiring. You turn the switch on, the lights turn on, turn the switch off, the lights turn off.

When you have more than one switch, you want any switch to "toggle" the lights at any time - if they're on, flip any switch and they turn off; if they're off, flip any switch and they turn on. As you'd expect, in multi switch circuits, switches are not labelled ON or OFF.

When there's two switches controlling the light, you use two three-way switches. Flip either switch to toggle the lights. The switches are called three way switches because they have three terminals to attach wires, not because there are three switches in the circuit. (Technically a three-way switch is a single pole double throw switch (SPDT) switch but again that term isn't really used in building wiring in North America. Everyone just calls them three-way switches.)

The wires between the two three-way switches are referred to as "travelers" and the other wire is referred to as the "common." The diagram shows the logical arrangement of the source power, the switches, and the load. The physical routing of the wiring may be much different depending how things are laid out. There are also some special purpose three way circuits that are wired a little differently.

When there's three or more switches controlling the light, you use two three way switches and one or more four way switches. Four way switches have four terminals. A four way switch is a variant of a double pole double throw (DPDT) switch, but again that's not really important.

Note that you can have as many four-way switches as you want between the two three-ways at the ends. You don't use five-way switches for four lights. The position of the terminals on the switches also varies - you have to check the instructions or markings on the switch to determine how the travelers are connected.

all of the switches would have the same symbol since they all connected to the same number of other switches

This is not true. Two of the switches are each connected to one other switch plus something else, and all the other switches are each connected to two other switches.

In effect the switches are connected in a chain, and together they make or break one path between the ends of the chain. The two switches on the ends of the chain each have another switch only on one side, while all the switches in the interior of the chain each have another switch on either side.

Here in the states, a circuit like you are describing would have a 3-way switch on either end and all other switches in between these would be 4-way switches. The electricians will be here shortly with possibly a better explanation and a wiring diagram.

This is how multiway switching works.

These are US friendly colors (regardless, colors tend to be a big mess in multiway circuits). Note the funny switch in the middle; it is different from the switches on the ends. The diagram may be a little unclear, the switch in the middle has 2 positions, either straight-thru or effectively switching the wires. The diagram erroneously shows the switch in the middle position, which is impossible.

There can be any number of middle switches. Each middle switch either reverses/exchanges the two wires, or sends them straight through. All wires are always connected.

So yes, a middle switch in a 3+ switch run will be weirder than the end switches.