I would classify things a bit differently than what has been said already, but I can certainly see the logic people are using.
Short range
These ships are carrier based or planet/station based. They can be heavy hitters or mass produced (cheaper) ships that give you the needed firepower for the craft/base size/mission/importance. Short ranged craft might need to fuel between planets once or twice, and multiple times going between star systems. Needs infrastructure in place or carriers to use. Infrastructure would be built up capability, or brought along such as Polaris, Starfarer, and Crucible support ships. Most fighters and single person ships are in here
Medium Range
Can go planet to planet and then back again easily, take a jaunt to the next star system, and in general, are sufficient for most escorting duties. These can also go into the star system between planets and explore for wrecked ships, mineral rich asteroids, etc. Freelancer, Connie Andromeda, Vanguard, Hull A (might be short ranged), B, and C and similar are here.
Long Range
Goes into the deep black between star systems, can looking for a new wormhole, and then through it to explore the system on the other side. Good crew facilities, possible medical bay, etc
Javelin, Idris, Polaris, Carrack, Caterpillar, Endeavor, Hull D, E, BMM, Connie Aquila (maybe), 890 Jump are ships that might fit this bill.
Light fighters
Cheap lightly armed craft with minimal armor. Often faster and more maneuverable than other ships. Often called interceptors.
Example: Gladius. Note, I would not classify the 300 series as a fighter, but if it was, it would be here).
Medium fighters
Moderately armed and armored ships. Slower than light fighters, faster than heavy fighters. A good balance of maneuverability, firepower, armor, and speed. Hornets, Sabres, Super Hornets, etc live here.
Heavy Fighters:
Heavily armed and armored fighters. Trades speed and maneuverability for firepower and armor. Vanguard Warden, Defender live here. Maybe the F8
Specialty Fighters:
Things that have specific uses or do not fit easily in the other categories. The Hurricane for instance is a light fighter except for the heavy armament. The Buccaneer would also fit here.
Light bombers/torpedo bombers:
Fighter types or size equipped with bombs. These are almost always short ranged ships and operate from carriers. A Gladiator is a light bomber
Medium bomber:
Craft designed to hit targets further out or carry a heavy payload than a light bomber. Can operate from carriers or bases/stations. An example might be a Vanguard Harbinger. Depending if you put a specialty bomber category in or not, the Eclipse might also be a medium bomber. Medium or short ranged
Heavy bomber:
Larger ship designed to launch multiple torpedoes/bombs. The Retaliator would be a good example of a Heavy bomber. These are often long range ships, but at the very least, they are medium ranged ships.
Multi-role:
These ships can do a lot of things. Explore, fight, bomb, smuggle, etc.
Aurora Connie, Cutlass, Endeavor, Freelancer, and Retaliators are good examples
Cargo Ships
Designed for cargo runs. Can be of any range. Caterpillar, Connie Taurus, Freelancer Max, Hull Series, BMM
Industrial ships:
Mining/reclaiming/fueling/repair ships go here. Examples are Orion, Starfarer, Prospector, Reclaimer, Crucible, etc.
Other:
Most includes specialty ships or ships that don't fit other roles. Reliant Sen, Genesis, combat drops ships, scout ships, snubs/parasite ships, etc, fit here.