Generally, any pen that holds, and automatically feeds, its own ink supply (including ballpoints, rollerballs, and stylographs). Specifically, a pen with an exposed or hooded split metal point, possibly with a hardened nib, fitted against a feed.
A fountain pen is a pen that contains a reservoir of water-based liquid ink. The ink is fed to the through a "feed" via a combination of gravity and capillary action. Filling the fountain pen reservoir with ink involves replacing a disposable ink cartridge, filling the pen with an eyedropper, filling a removable reservoir with a screw or piston mechanism (commonly called a converter), or using one of a variety of internal mechanisms which suck ink into the reservoir from a bottle through the nib.