The only known living natural vampire of this category
Hellsing vampirism is divided into two categories: "natural" and "artificial". They're mostly the same at first glance. They both retain the need to consume blood, they're both vastly stronger than the average human, and they're not as averse to sunlight as some other species are, though this can depend on the individual vampire's strength.
In BLN it's been shown that both natural and artificial vampires can only create new vampires by drinking the blood of a virgin of the opposite sex. Anyone who doesn't fall into that category who gets drained by a Hellsing vampire is instead turned into a ghoul: a zombie under the vampire's control.
It's unknown if artificial vampires create more "artificial" vampires via this method, or if the turned ones become "natural" due to the process.
What separates the two is how they're created and their own powers.
Artificial[]
An artificial vampire is created when a microchip containing DNA from Mina Harker is implanted in their brain. This results in their bodies slowly transforming into full-fledged vampires and they gain all of the advantages therein. No artificial vampire is weak against sunlight, or any other traditional vampire weakness, and they gain a unique power that is exclusive to that vampire in particular.
Unlike natural Hellsing vampires, it's canon in BLN that artificial vampires have a chance of returning to full humanity once their microchip is removed or disabled if they happen to survive the process of reverting back to a human state.
Natural[]
The "natural" vampires are brought about in other ways. The only way to become a natural vampire without being sired by an existing one is to be near death and desperate enough to drink blood spilled on a battlefield. There have only been two cases shown in Hellsing that fit this scenario: Alucard's origins, and one involving the Major, which he rejected.
Natural vampires start off as relatively weak, able to access the enhanced senses and strength of full vampires temporarily. However, they do retain most of the typical vampire weaknesses: they can't be out in direct sunlight without covering their skin, they have to sleep in a coffin at night, and so on. It's only when they willingly drink human blood for the first time that they lose these weaknesses and become stronger, gaining an individual power in the process. Theoretically, it's possible that they gain more powers if they drank more blood.