By ticking allow access to 'My Online Orders', you are giving the user access to the 'My Online Orders' section, meaning that they can place online orders through the 'My Online Orders' or 'My Quotes' section, or via product lists.
By ticking allow access to 'My Online Orders', you are giving the user access to the 'My Online Orders' section, meaning that they can place online orders through the 'My Online Orders' or 'My Quotes' section, or via product lists.