Please tell me the difference between not to do and don't do

Not to do is generally not used alone. One of the more common uses I can think of is:

He did A, not to do B, but to do C.

He did A, not to do B, but to do C.

For example, "He said that to you, not to make you feel ashamed, but to wake you up." He said that to you, not to embarrass you, but to wake you up. So simply put, not to do sth means not for something.

Not to do is actually the negative form of the infinitive to do, and to do alone is to do something. Not to be confused here with certain verb phrases. For example, in "want to do", "want to" is a phrase and cannot be regarded as "to do".

Don't do is very commonly used. Usually used in imperative sentences, meaning not to do something.

Don't drink that soup! Don't drink that soup!

Don't come back too late. Don't come back too late.

******************************************888

Okay, one last addition.

When used as warning words, the tone is very absolute, just like in Chinese, no xxx is allowed, xxx is prohibited

In English, no xxx is used directly.

No smoking.No smoking

No food inside the room. No parking 7 am - 9 pm. No parking from 7 am to 9 pm (here).

Sometimes you want to be polite, so use Do not.

Please don't bring food or drink into the lab. Please don't bring food or drink into the lab.

There is no separate use of not do in English.