Your reply describes the differences very well, Alisdair, I found another, more detailed one at
http://www.grahamrice.com/hellebore/species/niger/index.html , which said: 'To the botanist the features which distinguish H. niger from other species are the undivided bracts, the noticeably prominent elaiosome on the seeds which anyone sowing fresh seed will have noticed and the smooth pollen grains. To the gardener the large, pure white, waxy flowers carried singly on stiff upright stems and the dark, leathery, almost untoothed foliage make it easily distinguishable.'
My experience is that
H. niger always flowers earlier, I intended to take a photo of one in our garden (in Oslo), which has been in flower from mid-November, but I was too late, it's now covered in snow. I have only seen flowers on H. orientalis in spring here.