Why would two distinctly separate custom fields share the same options?
Civi allows you to set the same Options to be available on multiple fields. You do this by selecting an existing set of Options when creating the field, rather than creating a new set.

If you require different options for the second field then yes set that field to "Create a new set of options"

However that will mess with any existing data you may have. I would suggest you create a new Field with the new set of options, then, if required, you may be able to figure out how to review the existing data and use Batch Update via Profile to add the relevant data to the new field.