All stars move, but I guess you are saying that the movement is more obvious with (apparently) close stars. But in any case for Orion the difference is minimal. If you were looking at Orion right now and were then suddenly transported back in time a few thousand years, the only things you would notice would be a much clearer sky and Orion would be at a diffent angle. I doubt whether you could discriminate any visible difference in the belt stars.