Frigate Taxonomy

There are a total of 20 basic tech 1 frigates in the game, 5 for each race each designed with a role in mind, There are also 4 basic rookie ships that are broadly similar to frigates, so I'm including them here.

Racial Frigate I

• Rookie Ships: Impairor, Ibis, Velator, Reaper - frigate sized so I'm including them on the list, their main role is to give you a free thing to fly whenever you arrive at station in a pod. They come free with a (crappy) civilian gun and mining laser.
  
• Mining Frigates: Tormentor, Bantam, Navitas, Burst - get bonuses to mining yields and cargo space, great until you can get in a cruiser or mining barge.

Racial Frigate II:

• Light Combat Frigates: Executioner, Condor, Atron, Slasher - fast combat ships, useful interceptors because they're faster than other frigates, but they can't fit enough of a tank to survive for long.
  
• Exploration Frigates: Magnate, Heron, Imicus, Probe - Get bonuses to exploration probes and usually some extra drone space. The Imicus can field 3 light drones and gets a bonus to control range.
  
• EWAR Frigate: Crucifier, Griffin, Maulus, Vigil - Designed to support other ships with electronic warfare. The Vigil is especially notable because it gets a speed bonus which is as rare as hens teeth these days.
  

Racial Frigate III:

• Combat Frigate: Punisher, Merlin, Incursus, Rifter - Get to mount bigger and more guns, and more room for defenses and utility modules, these will be the staple of your Eve ship diet because they form the backbone of low level missions and tacklers in PVP. 
  
• Missile Frigate: Inquisitor, Kestrel, Tristan, Breacher - Favour missiles over guns, in the case of the Kestrel this is pure win and Caldari pilots favour their missile frigate over the gun oriented Merlin. The gallente Tristan however rather unloved because there's very few other gallente ships with missile launchers.

Beyond these basic ships there are a plethora of faction combat frigates, these are generally very expensive, but significantly faster and tougher and meaner than the plain old tech 1 versions on which they're based.

The 4 Empire faction frigates are the Imperial Navy Slicer, Caldari Navy Hookbill, Federation Navy Comet & Republic Fleet Firetail - they all need the relevant racial frigate skill at level 3.

The Pirate factions have their own ships too, all of these represent a merging of 2 races ship characteristics and thus need the pilot to be proficient in flying ships from both races. They are the Dramiel (angels), Cruor (Blood Raiders), Word (Guristas), Succubus (Sansha) & Daredevil (Serpentis) - and they're even more exclusive, and expensive, than the empire faction versions.

Finally, there's the Tech 2 versions of most of the basic ships, the tech 2 versions need multiple level 5 skills before you can fly them, but they are vastly more effective than the Tech 1 versions.

•  Interceptors are derived from the light combat ships, these are generally the fasted ships in the game and designed to catch and lock down enemy ships and stop them escaping
  
• Covert Ops are derived from the probe ships, they get the ability to warp around while cloaked and even better bonuses to probing.
• Electronic Attack Ships are derived from the EWAR frigates and gain more bonuses to a wider range of electronic warfare.
• Assault Ships take the combat frigates and make them even tougher, these can shrug off attacks and dish it out when needed.
• Stealth Bombers are the tech 2 versions of the missile frigate, these are greatly loved in 0.0 because they can sneak around cloaked and then drop bombs or attack large ships with torpedos, but, one good shot will kill them.

So, I think that's them all, I hope to follow up on this with some tried and tested fits, tactics and warnings about how to use these.