These two doesn't seem to play well together. Mean, both options are mutually exclusive: we don't want Online Registration enabled if Registration End Date is in the past, do we? Even if (not sure) by "Registration End Date" we mean an offline registration end date.
The checkbox that states "online registration is enabled" acts like a switch to enable online registration and allow you to configure the online registration parameters under the tab. If you uncheck this the fields will be hidden and online registration will be disabled.
The date fields set the start and end date that the online registration forms are available to visitors. This allows you to open and close registration at specific times automatically.
This all controls the public registration. nothing on this screen effects back end registrations.
Hope this helps.