Are vampires zombies or are zombies vampires?

So while my wife and I were watching Buffy the other day I started wondering "What if there were Vampire Zombies?" As in Vampires turned into Zombies. My wife said that Vampires already were Zombies because they are undead and feed off the living. But I said no, there are differences. Also I seem to recall there being vampire zombies in a recent game or movie. So what does everyone think? Are vampire zombies? Can Vampires turn into zombies and vice versa?

A vampire can't turn into a zombie cause its already dead, and a zombie can't turn into a vampire cause zombies can't get infected by the bite of a vampire.

Zombies are unintelligent and have only primal instincts at best. Vampires are charecterized by their physical features, including enhanced agility and strength, sometimes shapeshifting characteristics, and their intelligence, and often depicted as being afraid of sunlight (not always depicted as being killed by sunlight, some lore just says they fear it)

Someone could be one or the other, but not both at the same time. They are both undead and feed off the living sure, but that would be like calling a toyota yaris a ferrari, they are both cars that run on fuel.

The way I see it, Vampires suck blood and zombies eat brains and human flesh, I would say that there is a huge difference

And also, vampires can think and are smart, zombies are often stupid and cant think at all

A vampire is a zombie

" A vampire can't turn into a zombie cause its already dead, and a zombie can't turn into a vampire cause zombies can't get infected by the bite of a vampire. "