Those two sentences hold the same meaning. The sentence could be changed quite a bit compared to the ones you gave however, by changing just one word. "I'm determined to visit Japan no matter what THE cost" This sentence here can imply that you are determine to visit Japan by any means necessary not just money. For example you are so determined that you would quite your job, leave you friends, etc. The sentences you gave mainly imply that you would be willing to pay as much money as you needed to go.

They mean just basically the same.