Anything that comes from an LPC is a fighter, regardless of its role or armament.
I'm not sure if this is explicitly stated anywhere, but if it isn't it might be useful for it to be.
Ship sizes definitely don't have any indication of which ships are in which class, and it would be helpful if they did.
Mostly I manage this through familiarity, which is not really an option for new players.
For ships I'm not familiar with it comes down to size - how big something looks. And if that's not sufficient, how much certain hull mods cost to fit.
Neither are great options for newer players.
Something on the refit screen might be helpful.
And the icon with the number could then be repeated elsewhere as needed. 1 being Frigates, 2 Destroyers, 3 Cruisers and 4 Capitals.
May also be worth giving the icons for each class thier own colour, so text can be dispensed with entirely if it needs to be displayed small.