ordinance factories make missiles, which you design with that missile button down next to turrets and design. Fighter factories make special small combat ships that have special requirements that can fit inside boat bays and hanger decks on larger ships. Fighters have the advantage of not using up shipyards to be built, but they are horrible at fuel efficiency and are really squishy.
To make a fighter you design a ship with a fighter variant engine(which you specify when you design the engine on the bottom dropdown box), without a bridge, under 500 tons with only a certain weight in weapon systems and armor. You'll know a ship you designed is a fighter if it says it is on the bottom of the class summary.
P.S. Fighters do still have a crew, for me about 50-100 people. But you can cut down on crew quarters size by using the small crew quarters tech, the command module tech seems to work too, but I don't know if that has any other side effects.
Doesn't make much sense really, but I try to wave it off as the 'ground crew' for the fighter, with the crew modules just being extra life support systems to supplement the carrier's life support to account for the extra number of crew on the carrier that the fighter carries but is unlisted. Course that logic falls apart a bit when you pick up a fighter lifepod with 20 people in it, but I try to ignore that. I just say it's the ejection capsule. If the officer is in it it's all good if it's just crew I consider the officer to be dead in an otherwise empty capsule.
P.S. #2 I never did the ingame tutorial thing all I did was the wiki tutorial and I'm doing fine..