I think the price difference comes fromt he lack of support from Thomann - no shops, relatively few staff compared to a bricks and mortar shop. But buying over the web, from Japan or another country a long way away, it makes a lot of sense to go to Thomann.
One other issue is warranty support - probably not an issue for a mouthpiece or a box of reeds, but for a sax it's a big issue.
Make sure that Thoman will supply tax free to Japan. AND check import duty&tax/shipping/handling costs before ordering, these can soon eat up the price differences...