that's a different matter; that's another story
Used to separate a new condition from a previous statement, often after a conditional like 〜となると or 〜なら. Indicates that under the new condition, the situation changes.
I usually buy at cheap stores, but when it comes to gifts, that's a different matter.
He's usually quiet, but once he's had a drink, that's another story.
A fixed expression composed of 話 (story, matter) + は (topic marker) + 別 (separate, different). The phrase literally means 'the story is separate' and is used idiomatically.