Interceptors: Protect ships from other fighters and missles, trying to destroy them, also will get in the way of incoming fire to protect the ship.
Bomber: Ships that deal a lot of damange quickly but them don't do anything else until rearming, some are more suited as finishers, others as pressure, but most can work as both, just not as well, they will use missles, torpedoes or bombs.
Support Fighter: Focus on attacking ships, but lack firepower to cause any meaningful damage (even for a fighter) instead focusing against shields or causing EMP damage or both. Focus on causing flux on the enemy
Fighter: Focus on attacking ships, but will actually cause meaningful damage (for a fighter), good for stripping away armor, making the foe weaker to actual ships, also good at causing damage to hulls, can theorically overwhelm and destroy frigates without any bigger ship support (not all kind of frigates thought) focus on stripping armor from enemy
General fighter: Does all of the above, IE: Thunder. it has missles, PD and can also attack armor, and a bigger range, but will not do all of these things as well as specialized fighters.