“I told him not to do that” The above sentence sounds more natural than: “I told him to not do that.” Sometimes you’ll hear the second one, but not very often.

Hello Valentina, there's no difference in meaning. The first is more commonly used and sounds a bit more natural, in my opinion. Hope that helps!

"Not to do" is the proper one, that's all the difference.

there is no real difference in the two little parts of a sentence you supply on which you expect a comprehensive answer. "not to do" "there is not a lot to do" (incorporates 'not to do') you could not say "there is to not do a lot" (it sounds awkward it is not really incorporating the phrase it just ads 'a lot' on the end ) However you can say things like "I (x) him/her/them to not do (y)" but "I told John not to do that" is much more natural