wow Thank you both Michael and Mike ! I have been studying English for a long time but I totally didn't know [ any more ] can be different based on part of speech. Now I get it. Thanks for your feedback !

In my opinion, you are exactly right in your question . Note that you have one "any more", and one "anymore" + all one word. Have a look at https://writingexplained.org/anymore-vs-any-more-difference

But to your question, no, these sentences are not different in the meaning of "any more". She does not want any more contact with him = she had contact but doesn't want more (she doesn't want to contact him and she doesn't want him to contact her). She doesn't want to contact him anymore = she contacted him before but doesn't want to do it in the future (but maybe she is OK if he will contact her first).

thank you so much Mike !!!!!

I think these sentences differ because "contact" is a noun in the first one and a verb in the second. She doesn't want any more contact (noun) vs. She doesn't want to contact (verb) him anymore. Notice with a noun any+more can be used separately (She doesn't want more contact; she doesn't want any contact = OK). With a verb "anymore" acts as a single word (she doesn't want to contact him any = incorrect; she doesn't want to contact him more = not incorrect but sounds funny). Also in this case "with" will be used with a noun (I want more contact with him) but not with a verb (I want to contact him more)