This is just a quick summary of the different filling mechanisms for fountain pens. There are almost certainly a lot of minor details and machnisms I’m forgetting about (or straight out ignorning) here.
In general there are two kinds of filling mechanisms. There are the pens that have some kind of built in system for sucking ink into the pens and the kind where you stick some kind of cartridge into the pen.
The latter are either single use cartridges or a converter that let you fill the pen with ink from a bottle. Some pen use propretary while others use the the international standard for them.
Pens with a built in system are usually what we call a pison filler. It the same idea as most converters use. You have a sylinder, some kind of screw that moves the piston up and down. When you move it down it pushes ink or air out and when you pull it up it pulls in ink or air.
You also have some other systems with a similar idea to the piston like the ones the Conid pens use, or vaccum pens.
A third option that work with some pens is to just fill the whole pen up with ink and seal it off with some grease.