The original Hellsing anime, animated by Gonzo, is loosely based on the manga series of the same name for the first 7 episodes, but deviates entirely from the manga's story in the last 6 episodes due to the fact that the manga series was still ongoing during its initial airing. Hellsing Ultimate is an OVA series animated by Madhouse that started airing 4 years after the original anime initially finished airing in Japan and is a very faithful adaption of the manga series.
Hellsing and Hellsing Ultimate have vastly different tones as well. Hellsing takes itself very seriously while Hellsing Ultimate incorporates a fair bit of humor and light-hearted moments into the story to offset the bloody and gruesomely violent battle scenes.
