This might sound dumb but I am really curious
Well -- as it's Oswald Mosley and Henry Moseley, the answer is probably "nothing, except by accident and by dint of living around the same time." The two were no more related than a hypothetical John Smith and John Smyth might have been.
They both served in the First World War, in any event. In my entirely subjective opinion, the wrong one of them died there.