In X-Men Origins: Wolverine it's stated that Victor & Logan are "brothers".
Which parent/s do they share?
In the film X-Men Origins: Wolverine you see that Wolverine is originally known as James Howlett.
He sees his "father" (John Howlett) being killed by Thomas Logan, a man who works as a groundskeeper on his John Howlett's estate. James then extrudes his bone claws for the first time and kills Thomas Logan, who reveals that he is actually his father before he dies.
Thomas Logan is Victor Creed's father, but James' mother (Elizabeth Howlett) is not Victor's mother. It is not explained why Victor has the surname Creed instead of Logan.
In the movie "X-Men Origins: Wolverine", Logan and Sabretooth share a biological father - the groundskeeper Thomas Logan - and are therefore actual brothers.
This idea was based on the "Wolverine: Origins" comic book, in which Wolverine finally remembered his "true" past along with his real name... James Howlett. Over the years the two have had a long, varied, complicated relationship full of lies, half-truths and misdirection. I'll attempt to cover the highlights in this answer:
X-Men Comics (Earth-616)
Initially, writer Chris Claremont had intended for Sabretooth to be Wolverine's father, although that idea went back & forth for a while and was implied a few times but never said outright. In 1991, that changed in Wolverine Vol. 2 #41 when Sabretooth revealed this fact to Wolverine during a fight. S.H.I.E.L.D. and Nick Fury refuted the idea with a blood test, and the whole thing was kind of swept under the rug after that point.
In the original X-Men movie from 2000, Wolverine had never met Sabretooth before, although he also didn't remember his past so it's possible that was untrue. It's also unknown if THIS Sabretooth is the same character as the one seen in "Origins", as this more bestial version is never referred to on-screen as Victor Creed.
Wolverine: Origin (Earth-616)
After the events of "M Day", the 616 Logan apparently got all his real memories back. This led into the "Wolverine: Origins" arc of 2002, in which he remembered his "true" origins. Long story short, he learned that he was James Howlett, son of John & Elizabeth Howlett - plantation owners back in the late 1800s. There was heavy implication that he was really the illegitimate son of Elizabeth and the groundskeeper, a man named Thomas Logan that looked just like a grown Wolverine. Thomas Logan had a son named "Dog" Logan, who looked like a young Victor Creed. However, neither the illegitimate relationship nor Dog's identity were confirmed, so both are left to speculation.
Ultimate Comics (Earth-1610)
In the Ultimate universe, Sabretooth was a Weapon X assassin who always felt inferior to his predecessor Wolverine. He destroyed all records regarding Wolverine's past, but later claimed that he was Wolverine's biological son. Wolverine stated that his scent said otherwise, so - again - we are left not knowing the truth.
Wolverine: Evolution (Earth-616)
In the 2003 comic arc titled "Evolution" (Wolverine Vol. 3 #50-55), writers again tried to clarify the relationship between Logan and Sabretooth. In this arc, a villain named Romulus led Sabretooth to believe that both he and Logan - as well as other wolf-like mutants - were the descendants of an ancient feral race divided into two opposing packs (or "tribes", if you prefer). Romulus claimed that Logan & Sabretooth were the "alphas" of the two groups, and therefore genetically fated to fight until one submits to the other. Romulus turned out to be both insane and a fraud, although another character claiming to be his sister later stated that he made the whole thing up and had planned to CREATE the lupine race using Wolverine and Sabretooth as genetic templates.
X-Men Origins: Wolverine (Earth-10005)
In the 2009 film "X-Men Origins: Wolverine", Logan and Sabretooth/Victor Creed are explicitly shown to be half-brothers that share the same biological father. The film essentially uses the same scene/plot as the "Origin" comic, but confirms the relationship that the comic only implied.