OTL was saw the Russo-Japanese Agreement of 1904, in which Japan recognized Russian dominance in Manchuria and Russia recognize Japanese dominance in Korea. This set the stage for Japan and Russia to annex Korea and Manchuria respectively in 1910.
Czar Nicholas had contemplated pushing the Japanese to recognize a neutral zone in Northern Korea. The Japanese were none too pleased and threatened war over such a thing. While the Russians were confident they could defeat Japan, they figured it wasn't worth the effort and accepted a straight recognition of Japanese domination in Korea.
What if they'd gone to war? Both sides would end up racking up big debts that would limit their expansion overall, I think. On the other hand, lessons might be learned by the belligerents that could have been quite put into effect during the Great War.