What are the different classes of capital ships and what are their roles?

Capital Ships:

Carrier class: Thanatos, Archon, Nidhoggur, Chimera.

I think people tended to use these mainly for logistics (i.e. moving goods outside Empire) and repairing POS'! However that changed when CCP nerfed their carrying abilities. However they also changed the way triage works, so they became more viable in the role which CCP originally intended.

Dreadnought class: Moros, Revelation, Phoenix, Naglfar.

Prior to the introduction of Fighter Bombers, Dreads were the mainstay for capital blobs. Their intended role was taking down POS' but they were also damned good at dropping other capital ships. Rightly or wrongly i think people view now as obsolete due to the changes to Motherships and Fighter Bombers (they eat Dreadnoughts!).

Freighters class:

I won't go into much detail here as some people dispute these ships as being capitals. However in my opinion they're capitals as they require the capital ship skill! They're used for hauling large amounts of cargo. Jump Freighters come complete with their Jump Drives, which makes moving items outside of Empire a lot safer. The introduction of the Jump Freighter pretty much made the Carrier obsolete in terms of long haul cargo movement.

All Capital class ships can dock in a station.

Super Capital Ships:

Motherships (or Super Carriers): Nyx, Wyvern, Hel, Aeon.

Originally these ships were much maligned for their lack of direction. CCP addressed by removing things like the Clone Vat Bay, increasing their EHP and introducing Fighter Bombers. They were a bonafide “i-win” button; however CCP recently balanced Fighter Bombers by changing their output from missile to turret. This introduced tracking and stopped the Mom from rolling everything in its path (well a little bit).

Titan class ships: Erebus, Avatar, Leviathan, Ragnarok.

I believe the Titan was first introduced to counter the dreaded 0.0 blob. This vision was realised via the grid wide Doomsday a Titan could deploy. There fun and games to be had when Titans could fire these remotely… hehe! However it was considered overpowered, so the AoE Doomsday was struck wtfbbq damage by CCP(dev_dude), and reduced to a single shot.

This was introduced with the unintended issue of being used in low sec, whereas the AoE could only be used in 0.0. Cue howls of protest and eventually patched this. There was also a huge outcry from Mom pilots as this weapon change was implemented without the complimentary increase to a Mom’s EHP. This resulted in Mom’s being one shotted by a Titan and the obligatory howls of protest.

The Mom got its EHP boost and can now survive one or two hits from a Doomsday device. Dreadnoughts and Carriers tend to be easy prey… The weapon cannot be used on structures.

Super Capital class ships cannot dock at a station.

So, what differentiates a Capital class ship from a Super Capital class ship? Well I guess the ability to dock, skill requirements, ease of production and cost. Each has its own effectiveness in its own role, so I do not see that as a defining factor in terms of Capital class versus Super Capital class.