ずにはすまないWon't get away without, Won't get off without, Have to, Have no choice but to, Can’t not

Both express necessity, but the source of that necessity is different. ずにはすまない means ‘cannot avoid doing’ and implies moral pressure, social responsibility, or consequences that make inaction unacceptable, often based on feelings or circumstances rather than rules, as in 迷惑をかけた以上、謝らずにはすまない ('Having caused trouble, I can’t avoid apologizing.'). なくてはならない expresses objective or logical necessity such as rules, requirements, or unavoidable conditions, without emotional pressure, as in 10時までに行かなくてはならない ('I must go by 10 o'clock.').

Both express that an action cannot be avoided for similar but slightly different reasons. ずにはすまない means ‘cannot avoid doing’ due to moral obligation, responsibility, or consequences, often implying inner pressure or remorse, as in 迷惑をかけた以上、謝らずにはすまない ('Since I caused trouble, I can’t avoid apologizing.'). わけにはいかない also means ‘cannot do,’ but focuses on social rules, common sense, or one’s position making the action inappropriate, rather than moral necessity, as in 今日は大事な会議があるから休むわけにはいかない ('I can’t take the day off because there is an important meeting.').