So I’ve read quite a bit of the articles and posts about transferring Yen with TransferWise or other things. But do you transfer the foreign money back into your own bank? Or does it have to be a different bank? How exactly does it work? The websites are also not as clear about transferring money, such as if it’s possible to just exchange it into the correct country’s currency and keep it in your account instead? I’d just like to know how it works completely 
I think you’re referring to transferwise borderless account which is a new feature.
They promise you’ll be able to open an account to hold electronic money similarly to a regular bank.
I checked it up but it doesn’t seem to be available in japan yet.
As far as I can tell at the moment your best option is to transfer from a japanese account you own to another account of your choice. You can also send to places like revolut, monzo or the like