What are the differences between "seems not" and "doesn't seem"?

Solution 1:

I don't think they are correct, close and understandable but not how a native English speaker would say it, I would say

• "He seems to not want us to help" and
• "He seems to want us to help"

negative questions are usually confusing so I'm not sure I can help you there.

• "It seems to not be working for me"
• "It doesn't seem to work for me" would be the same meaning.
• "It seems to not be working" would also be the same though applied to 'it' not just you working 'it'.

I think the difference is perhaps when spoken rather than written sometimes people miss/slur ot half say things as there is a lot more context.