This is not that simple to answer. Grammatically, they are the same. So your assumption is not correct. ~なくてはなりませんmeans that it must be so-and-so, because of the law, rules or something external, not because you think so. ~なくてはいけませんhas the similar meaning, "it must be so-and-so" except that this is more of an opinion of the person who said this. I hope this helps.