Are Vampires and zombies the same thing? Well, yes and no.
According to The Vampire Slayers' Field Guide to the Undead
by Shane MacDougall, an excellent reference in these matters, there are astral vampires, essential vampires, living vampires, human vampires ( people who think they are "vampires"...can be found at goth clubs...) and psychic vampires, none of which have ever been "dead".
Now the other type of classic vampire is called a "revenant" and is a corpse that has been reanimated and risen as a vampire, ghoul, zombie or ghost that feasts on the blood or flesh of the living. In this case what we know from the movies as 'zombies" and what is known in European folklore as "vampires" are rather closely related. They shamble and show signs of decay. Nasty creatures.
Now true zombies are a Haitian phenomena where a houngan uses a combination of black magic and poisons to turn a person into a zombie. The zombie is not really dead but the illusion is so real that they are often buried alive, only to be later dug up by the houngan and put to work in the fields as a virtual slave, kept "zombified" by the continued application of certian poison potions.
Conversely, the classic vampire of literature ( such as Stoker's DRACULA) is a crafty shape-shifter who is intelligent and evil, but doesn't have much in common with a "zombie". Werewolves, also being shape-shifters, have much in common with this definition of the vampire.
One thing is certain. These creatures exist. Watch your ass out there. The devil's work is everywhere.