The Other Provider status has the exact same effect as the Inactive status. The one difference is that if a Client is updated to Other Provider, you will be notified that the Client has opted to receive their care from another provider.
If a Client is updated from Active to Other Provider and they have current Schedules on their Profile, all future Tasks associated with these Schedules will be cancelled. You will not be able to reactivate these even if the Client is later switched back to Active.