The ships are the classes.
Your character can train whatever skills you want, to unlock whatever ships you want (and their weapons and associated defensive modules). Each ship is intended for a role (DPS, Tank, Electronic Warfare jamming (Crowd Control), remote repair Logistics (healing), scouting, mining, transporting materials, etc.).
Your character can train multiple ships, but at any point in time you can only fly one, so you’re basically respeccing your “class” every time you undock, by the choice of ship you choose to undock with. Thus, compared to other MMO’s, when you build a character here, it’s the equivalent of an account full of warriors, mages, rogues, etc. in other games. Because you get access to all ships / all classes, if you want to. It just takes equally as long to do them all at once.
As far as frigates, destroyers, cruisers, battlecruisers, battleships, and capital ships, the basic roles (tank, DPS, ewar, logi, scout, etc.) are represented with each tonnage class, but, of course, heavier ships offer heavier tank and DPS values, at the expense of mobility. Frigates, for example, actually get damage reduction from various big weapons by virtue of just being fast and small, but you’ll need a wolf-pack fleet to attack a battleship because a single frigate will survive the return fire from the battleship (by being small and fast) but won’t be able to scratch battleship-grade shields or armor.
So the parallels with other MMO’s only apply up to a point.
In general:
Tech 1 ships are designed to be versatile. There are quite a few frigates, cruisers, and even battleships that you just dock, re-fit with different modules, and voila the ship now has a different role. No need to change the ship itself.
Faction ships (Navy Issue) are extremely expensive, improved versions of Tech 1 ships. Ship balance is done very tightly, and so the fact that a Navy Issue ship may have 1 extra mid slot compared to the regular ship, makes a big big difference. You pay for the extra slot with hundreds of millions of ISK, so it may not be worth it until you simply have no other options (skills are maxed, you’re already using top grade shields, etc.).
Tech 2 ships are super-specialized. This is where the fleet commander (FC) decides “I want a tank, 3 DPS, 2 scouts, 2 logi, and 2 ewar”, and puts together a fleet with ships that are super-specialized to those tasks. Tech 2 ships perform better at their specific task, but otherwise gain huge vulnerabilities to all other tasks, that require a fleet for support and protection (healer without a tank = toast, basically).
Tech 3 ships are gimmick ships; they have some sort of ability of power that comes with the ship itself, rather than the modules that you put in it, and usually the gimmick requires a fleet to “prepare” the battle scene for full effect.
Capital ships are NOT intended to be flown solo, even though people try. They move by “jumping” to cyno beacons that must be activated at the intended destination by someone else (or by an alt), and in general they are intended for heavy firepower to destroy the millions of hit points that citadels and other player structures have. Their weapon tracking is so bad that pretty much they can’t hit anything else; they even have trouble hitting battleships. The ships are generally too expensive to be funded solo, and are typically used like in the Navy, where the captain doesn’t own the ship; the alliance does.