The custom Nintex fields do not become SharePoint columns. If you have a SP column you could create a field and connect them though.

In addition, if you create the Sharepoint columns first and then reload the form designer, these newly added columns will appear as controls that you could then drag and drop onto your form.    

to create sharepoint's list fields directly from designer note te 'Create Coulmn/ icon on the ribbon.

I see the fields on the selection window on left but the field is not visible in the pull down in the field settings to make the connection - why?