Same answer as Arnoud Buzing
Another way is to go to "Preferences" -> "Advanced" -> "Open Option Inspector".
Search for CellContext and set the option from "Global" to "Notebook"
Another possibility for clearing out definitions is to use the old package CleanSlate by Todd Gayley. See: https://library.wolfram.com/infocenter/MathSource/4718/
When you closed your notebook without saving did you have another notebook open? Or a Help page? Closing a notebook is not the same as closing a Mathematica Session. If you want to start over then close everything and start a new Session.
I just did two tests. I brought up an existing notebook, evaluated it and noted the last In/Out numbers. (50, 51, 52). In one test I saved it and closed it. In the other test I didn't save it before closing. These actions ended the Mathematica Session. I then started a new notebook and typed the statement 1+1 and evaluated it. In both cases the In/Out numbers were (1,2).
When I do development in a notebook I always use Sectional organization. Then if I end up in a rabbit hole I just start a new Section and delete the old Section and continue with the same notebook. Often I still want to copy over from the old Section. Sometimes I name them Try 1 and Try 2.