Unsubscribing a contact from a list blocks emails for that list, but allows the contact to receive emails for other lists.
For example, if a contact no longer wants to receive promotional emails, but still wants to receive newletter emails, then they could be unsubscribed from the promotional list, but still subscribed to the newsletter list.
If a contact is unsubscribed from an existing list and imported/added to a new list, then the contact will receive email sent to the new list (unless the contact is set to Do Not Email).
Setting a contact to Do Not Email blocks all future emails regardless of whether they are subscribed to a list.
If a contact is set to Do Not Email and imported/added to a new list, then the contact will NOT receive email sent to the new list.
Note: If the contact does not want to receive any future emails, then the contact should be set to Do Not Email instead of unsubscribing the contact from each existing list.