Does that make a bit more sense..?
Not really but I suspect that you are UK or EU.
Wire color codes are different than US.
So is terminology.
My apologies.
What US calls a 3-way switch, I believe UK calls a 2 way.
UK has two wiring color schemes. In both schemes the white is neutral as in the US. Green is ground or earth. That the important parts. Other colors are hots.
We will talk neutral and hot. We will talk logic The green (earth) is for safety. It is connected to all surfaces that can conduct current. It is not part of the circuitry.
A single pole switch either makes contact between the two terminals or it does not. A 3-way (your 2-way) makes contact between the common terminal and L1 or it makes contact between the common terminal and L2 depending on its setting.
In US, the single pole switch has an ON and an OFF embossed on the switch toggle handle. The 3-way (your 2-way) does not.
Three way (your 2-way) switches have become so inexpensive they are sometimes used like a single pole (ON_OFF) switch. When this is done, one conductor is connected to the common and the other conductor is connected to either L1 or L2. It doesn't mater which. The remaining terminal (L1 or L2) is left unused. When wired this way, it functions just like the single pole switch. It is either ON or it is not.
There are two ways to wire a light with a switch.
The first and most easy to comprehend is called "feeding the switch". Power, both hot and neutral, are brought to the switch box. Here, the incoming neutral is connected to the neutral going to the light fixture. The incoming hot conductor is connected to one of the terminals of the switch. The hot conductor to the light fixture is connected to the other terminal of the switch. When the switch is in one position there is contact between the two conductors and the light burns. In the other switch position there is no contact and the light does not burn.
The second way of wiring a light and switch is called "feeding the fixture"
When wired this way power, both hot and neutral, is brought to the light fixture box. Here the neutral is connected to the neutral of the light itself. The hot is connected to one of the wires going to the switch. In US, it is the convention to use the white wire to go to the switch and the black for the return from the switch. Although it is often not done, you are required by code to color both ends of the white to some color other than white or grey, to signify that the white has been re-designated as a hot conductor. The return from the switch (black in the US) is connected to the hot of the fixture itself.
At the switch box one conductor, doesn't matter which one, is connected to the common and the other conductor is connected to either L1 or L2, doesn't matter which. These conductors are called a switch loop. So, power comes to the fixture box, goes on one wire of the switch loop to the switch box, goes through the switch (when ON) and returns to the fixture on the other wire of the switch loop.
From what you have told me, this is what your wiring sounds like. However, I can think of no reason to have a "pig tail" of jumper wire between the two switches.
Suggest that you determine which white wire goes with which red wire. Connect the white to the common and the red to the L1. Do the same with the other set of wires and other switch and see what happens.
The worst thing that can happen is you trip the breaker.
On the back of this switch is the are the 2 gang boxes, each one with a terminal marked L1, L2 and C
That means you can connect two cable if need be, Pick one and use it for you connections.
If you can provide any more information or have any questions, post back. We will see if we can figure it out together.
Don't like being so verbose but wanted to be detailed and specific.