I feel depending on where I put "not", the nuances of the sentences are quite different. When we put "not" next to a verb, it is likely to put more emphasis on negative meaning.
I don't do many things at home.(emphasis on negation)
I do not many things at home.
There aren't many things that I do at home.(emphasis on negation)
There are not many things that I do at home.
Am I right? or Aren't there any differences?