Thanks for your answers. The last picture explains a lot, based on a picture search I see that they're often sold together. Unfortunately in the one I bought, there wasn't any other chuck included (see picture of box). Because I bought both together (promotion at a supermarket) I made the wrong assumption that the drills would fit in...
After some more googling my understanding is that the other chuck is put in/on the SDS-quick. I cannot find the exact chuck which is pictured above, but the professional or SDS-plus also seem to fit, so I'll give that a try.
Thanks again, I did a lot of googling but without knowing what exactly to look for I couldn't find any answers and this forum was my last hope :-)