Simplified and traditional characters have different unicode codepoints. Japanese and mainland simplifications have different codepoints when they differ, and Japanese-only characters of course have their own codepoints.
The argument is about characters like 冷. It is given a single codepoint, but Chinese typefaces draw the bottommost stroke diagonally, and Japanese typefaces tend to draw it vertically. (When writing it by hand, both versions are acceptable in Japanese also, http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q105... )
The argument is about characters like 冷. It is given a single codepoint, but Chinese typefaces draw the bottommost stroke diagonally, and Japanese typefaces tend to draw it vertically. (When writing it by hand, both versions are acceptable in Japanese also, http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q105... )