Two adaptations of the original Tsukihime Visual Novel exist - an anime and a manga. In many ways they appear to be quite similar - adapting the Arcueid route while adding some elements from the other routes to get across a story that ends conclusively rather than one that can feel satisifying and leave loose ends for the other routes to deal with.
Despite this, they have polar opposite reputations.
A managa adaption drawn by Sasaki Shounen that ran from 2003-2010 across 10 volumes and 74 chapters.
The Tsukihime manga is a generally respected adaptation of the Arcueid route. The basic premise therefore is the same as the Visual Novel - boy meets girl, kills girl and discovers she's a vampire.
The difference between the VN and the manga is largely in the presence of elements borrowed from the Ciel and Akiha routes to flesh out characters not covered in depth in the VN's Arcueid route, like Tohno SHIKI, Akiha and Ciel.
It manages to find ways to naturally insert these, like giving Ciel more time and stuff to do in the Nrvnqsr fight compared to the VN, extending the flasbacks to Shiki and SHIKI's childhood and having Roa's control of SHIKI be a more gradual process.
The art is great too, going from warm and inviting, to cute, to more threatening depending on the scene.
The manga Sadly only ever had 6 volumes produced in English and the scans used for some of the later volumes by scanlators weren't the best. A high-quality offical scan exists but is in Japanese only. The scan is on bookwalker.jp and can be accessed via Type Moon Comic Ace website via the link placed there.
There is no Tsukihime Anime
Released during 2003 and animated by J.C.Staf.
Also an adaptation of the Arcuied route, but far more hated by fans to the point of some refusing to admit it exists.
Much maligned for its poor animation quality, rushing of the plot to fit everything into the number episodes, just not having appealing artwork, undercutting dramatic moments by cheaping out on them and managing far poorer than the manga in adding in more elements to flesh everything out - with a filler episode at a theme-park, brief mention of the Tohno blood stuff and Roa looking like SHIKI in bandages.
It was previously released in the UK by MVM, but the license must have expired as it is no longer in print and must be bought second-hand from sites like CEX. It stands to reason the same is true of other nations like the USA or Canada.