不一样. under the condition 在该情况下, on condition that 在某某条件下 under the condition, we have no choice but to comply 在那个情况下,我们有没有选择,只能遵守 I will lend you the money on condition that you return it tomorrow 我会借你钱,条件是你明天把它还给我
under/ on the condition在这(那)种条件(情况)下; on condition that..(后跟从句) 条件是…… He is a blind man. It is very hard for him to walk on streets on/under the condition. You can go now on condition that you have to finish your homework.