Well, there's a lot of vast differences between Vlad and your typical vampire. The only thing they really share are a few asinine personality traits:
- A love of killing (usually)
- A thirst for blood
- The usage of blood in magic
To tell the difference between your typical vampire and Vladimir, we have to look at the generalizations made of vampires themselves, and define what sets Vlad apart in each of these.
1) Vampires consume blood
I can't say for sure whether Vlad does this or not. It's not directly stated that he consumes blood, but looking at the icon for his passive, one would think that he does.
However, unlike most vampires that we know - the famous Alucard included - Vlad doesn't have to get close to his target to consume their blood. He seems to be able to draw it out from within them, using his magic. This is very unusual among vampire-kind as far as feeding goes. Even though the manipulation of blood (moving it around in the air especially) seems to be a common power, it's reserved for very powerful vampires with a strong magical connection to it, drawing it in to heal themselves or harden it into weapons. I have yet to see a vampire actually feed off this manipulated blood, which would make Vlad a first.
2) Vampires use this earned blood to create magic
We don't know yet whether or not Vlad's consumption of his mentor, Dmitri, gave him his present powers. What we do know is that most of vampire-kind improves their abilities based on how much blood they have consumed, thus how much blood they have available for use. It's implied that, to vampires, the more blood they have directly equates to their magical capabilities, as if blood itself has a kind of magic to it.
Vlad doesn't seem to operate in this way. His whole shin-gig seems to be that blood > health, not that blood > magic. His "magic" is in manipulating blood, not that blood makes magic available to him.
3) Vampire magic is very much magic
Vlad is quite the contrary to this. Vlad does not use the power siphoned from a large blood store to use alternate spells. Read over his kit once more, my friend; as a necromancer uses all things related to death, a hemomancer uses all things related to blood. Vlad does not have a bat shape - he cannot fire Lux lazors, melt into shadows, cast fireballs, or entrance you in winding chants as you stare into his eyes. For goodness sakes, his ult infects you with a blood-borne plague! Nothing he uses is what we would call "magic." It is all VERY blood-specific.
4) Vampires are cursed by hellish magic to become a "vampire"
No where in his lore does it say that Vlad was cursed. If anything, he's just a demonic individual who revels in bloodshed. He murdered his childhood friends** just** to watch them bleed. Sick, right? His profile still says that he is human, as opposed to Ryze who is "formerly human." Vlad is a mere practitioner of Hemo-, or "Blood" magic; thus making him a hemomancer.
- tl;dr Vlad manipulates blood in a way that seems magical, but in the end is just the flat usage of blood alone though a bond. He doesn't use magic as we know magic; thus we can assume he is not a "mage." He is a "hemomancer" - whatever that is. It's heavily inspired by vampirism, but is still not vampirism as we know it, thus making the different title valid and necessary.