Vampires are all undead, yea. The Vampire Counts do play different to Coasts though, as they have no ranged, whereas the Pirates have one of the best ranged rosters in the game.
The Counts might have a slightly more vampire theme but, not by much; they only have 2 beasts (Vargheists & Varghulfs) and 1 cavalry (Blood Knights) that are more "vampire-ish." The Vamp Coast Depth Guards are just dismounted Blood Knights, so, I guess you could say, that's mostly a wash. AFAIK, Vampires in Warhammer, generally, do not serve as rank and file troops, but as commanders. That's why they are lords and heroes.
Undead are not the most friendly of races to play, as their mechanics and tactics are a bit different to the living races. You need to build heroes and lords heavy for leadership, and micromanage army placement on the battlefield (stay in leadership aura's). Almost every undead unit has fear or terror though, so it can come down to a game of, route them, before your army disintegrates. Resupplying in the field, at large battlegrounds is huge, and can make up for the heavier losses the undead usually take.
As for the Vamp coast ship, it's awesome when used as support (this goes for Dark Elves too). Fully upgraded, it gives you 3 spells to cast, anywhere on the battlefield, to soften up incoming enemies. I build the ship for full support, for army buffs; one of which gives large boost to army replenishment that makes a significant difference when campaigning.
Steam has a bunch of guides where you might be able to get a rundown for each race, before playing, but I haven't seen anywhere that gives an overview of mechanics and a quick start guide.