Default = Default Permission set on that folder for authenticated users
Anonymous = Permission set for external, non-authenticated users
You don't want to change those defaults typically for a user mailbox.
If you were to set Default to Owner, any user in your org could, in theory, open your inbox and have full access to it.
Same with anonymous.
Its not common to delegate any folder but your calendar. Often, users set their calendar to Default Reviewer so anyone in the org can view it.
Delegates who need higher permissions are then added explicitly.