I was busy for a different reason today, but not because of work.
He's famous for another reason, not because he's popular.
この場合、次のような言い方ができますよ。
ーI was busy for a different reason today, but not because of work.
「今日は違う意味で忙しかったが、仕事ではない」
for a different reason で「違う理由で・意味で」と言えます。
ーHe's famous for another reason, not because he's popular.
「彼は人気があるのではなく、違う意味で有名だ」
for another reason「別の理由で・意味で」と言えます。
ご参考まで!