てはいけません＝showing<general rule> ＊主に禁煙の看板など。mainly used for sign board (Smoking is forbidden.) ＊2 子どもなどには言うことができます。 You can say 「〜てはいけません」to children.Because some children don't know about general rules. But if you say「〜てはいけません」to adults,it sounds very rude. ないでください＝request ＊人の行動をやめさせるときに使います。 used when you want to stop someone from doing〜 therefore in this case below,you can use both 「〜てはいけません」and 「ないでください」in the same conversation. A:この部屋では本当はタバコを吸ってはいけません。A:Actually,Smoking is forbidden in this room.(showing general rule) でも今日だけは特別ですよ。タバコを吸ってもいいです。But just today,you can smoke. ただし、床にタバコの灰は落とさないでください。However,please don't knock the ash off your cigarette to the floor.(say request to stop knocking the ash off the cigarette)

This is an interesting question! I feel usage of these constructions are same, but there is a subtle difference in exact meaning of sentences(though we don't care in daily life). ここで写真を撮らないでください >>Exact meaning : Please don't take pictures here ここでたばこを吸ってはいけません >>Exact meaning: It's not allowed to smoke here, or You can't smoke here Vないformでください is more like you are asking someone not to do things, Vてformはいけません is like you prohibit someone to do that action.

Both mean almost the same, "don't do that". The purpose is, however, slightly different. ～Vしないでください　： don't do it for me/us/people ～てはいけない ： don't do it. It is not the right thing to do. 「ここは子どもがいるんです。熱のあるひとは、入ってこないでください！」 「非常事態宣言が出ている今、用もなく街を歩き回ってはいけません」 ---------------------- くださる： polite form of the verb くれる(give). ください： imperataive form for くださる いけない： literally "it can't go" Aしてはいけない： literally "if you do A, it can't go", "doing A won't let it go --> doing A won't get you anywhere".