Hi Attila,
Japanese winterberry is also Japanese Holly, just a deciduous holly. I'm not sure if by 'Japanese Holly' there is any more meaning than what people have simply commonly referred to what is often used for landscape plants - Ilex crenata. However, in bonsai circles, Japanese holly is commonly referring to Ilex Serrata. In both instances, these are just culturally descriptive names, not botanical references. If you are looking for botanical correctness, then both are Ilex (holly) and are both considered of Japanese habitat. Serrata is a deciduous holly and is also a Japanese holly. So the confusion is only whether one is referring to the Crenata or the Serrata. Both are hollies. Whether one is culturally referring to the Crenata more often as 'Japanese Holly' is almost meaningless to some - I've always personally considered Ilex Serrata (or umemodoki) to be 'Japanese Holly' - then again, I have never grown Crenata as either bonsai or landscape so it is not in my common reference. I'm not trying to make an issue of your question / comparison - just showing that there is a difference in what a 'name' is and what it really means or is just culturally referring to.