Thank you very much for the help Evan!

But I'm not sure what is common at you in the US is also common here at the other side of the pond.
You said flushed door is the common.
But rebated is the overlapping one.
Here I have this door, which looks overlapping to me, but this is the common one here. So now I'm still confused :S
This is the common type here. I believe it's rebated. But I'm not sure? Maybe it's neither of those 2, but a 3rd type?
Anyway here is photo of my opened door's side: (It's pretty thick...)

And here is a photo of the passing door frame and the wall from the inside:

Sorry if the photos are big.
I'm not sure can id be clearly established what kind of door is this or shall I take another one?
Apart from establishing what kind of door it is, I'm starting to believe one cannot actually put a traditional deadbolt in it at all, due the the structure of the door.
It is covered by wood, but I believe there is both metal parts and layers of plastic inside. Also it closes at 3 point on 1 side instead of just 1.
What is a professional's take on that one?