I don't know specifics re South Korea and Greece but I wouldn't be surprised if what counts as suicide in one country might count as accident or unknown cause of death in another which makes comparisons a bit tricky.
And that is a big difference - Christianity views suicide as disgraceful, punishable, and cowardly. Seppuku on the other hand is honorable and courageous. I've also heard of older Japanese committing suicide to ease burdens on the next generation. I would imagine just this difference in perspective would lend itself to very different rates all else being equal.