Me and my friends are having somewhat of a debate to find out if a vampire is a type of a ghost or not. I am convinced that vampires are a kind of ghost, yet they are not the exact same thing; as how a lion and tiger are still different, but from the family of cats. Is a vampire a type of ghost?
TL;DR: No, vampires are not ghosts.
Because the question is so broad, it is very difficult to say anything more with any certainty. Therefore, I am forced to rely, for the time being, on the broadest definitions of the vampire trope, from the Southeastern European pre-18th century folklore from which the modern trope has primarily evolved.
Key difference: Ghost and Vampire are both considered to be supernatural beings. The main difference between the two is that vampires are considered as mortals, who live up-to 1000 years, whereas ghosts are the soul and spirit of the deceased.
- Difference Between
The claim that vampires live for up to a thousand years is apparently based on folklore rather than modern vampire fiction. In most modern works of fiction, including, most importantly, Bram Stoker's Dracula, vampires are effectively immortal, and can only be killed through specific means (e.g., a stake through the heart, exposure to sunlight, or fire).
The site linked above features this chart showing the differences between the vampires and ghosts of folklore: