The term convertible refers to a hood that can be installed in different ducting modes. Typically a convertible hood can accommodate: 7" round ducted, 3 ¼" X 10" vertical or horizontal ducted and non-ducted applications available at installation.
A convertible hood has both ducted and non-duct features built-in or the appropriate parts are provided in the box at the time of purchase. Therefore you have the option to install it without the additional purchase of special parts or kits. However, the charcoal filters needed for a non-duct hood may need to be purchased separately.