I bought a pair of two way switches before Christmas and the marking were not plain so got the instructions to identify common. The instruction did show a two way diagram and how to wire it to light either of two lamps. This is two way but not as we would normally use the switch. OK for me it showed which was common but would not help the normal DIY guy so I can understand errors.
When most people refer to two way it is to use two way and intermediate switches to control a single lamp.
Two way refers to the switch it has two positions you could get three, four or more way switches but in the main these would be rotary and no real use for two way lighting. So any attempt to look up three way lighting is likely to find the wrong results. However many switches it's still two way.
Many a DIY guy does not realise that centre switch is different. I have seen it time and time again where some one has the wrong switch so can't work out how to wire it. You will have 2 x two way switches and as many intermediate (cross over) switches as you like. An intermediate can be used as a two way but not the other way around.
Of course it may have never been designed as two way. Or it may have been altered. The two way system needs three wires (plus earth) between the switches. Years ago it was common to borrow the line from another switch so getting away with two wires. However to do that both switches would need feeding from same fuse/MCB and also it can cause main hum on radios etc.
Where the up and down stairs circuits have been split often this means you can no longer use just two wires. Before the fitting of RCD protection people would ignore the rules but with RCD protection we are forced to follow the rules or the RCD will trip. One way around the problem is to wire switches in parallel instead so either can switch on the light but you need both to be off to switch light off.
Times have moved on and there are now radio control switches which can work lights in the same way as old two way switching a little more expensive but gets around the having to install new cables.
Once you post pictures we should be able to work out what you have.