Steve and Bucky
Relationship in the Comics
Bucky and Steve are canonically best friends in almost every version of Marvel canon. In fact, in the comics, Steve often can't think of anything or anyone but Bucky. Sometimes they spend whole issues calling for each other. When given the chance to go back in time, Steve would gladly sacrifice everything he has just for a chance to be with Bucky again. Even in alternate universes where Steve is turned into an angel, nothing can keep them apart.
Relationship in the Marvel Cinematic Universe
Within the Marvel Cinematic Universe movieverse, Bucky and Steve are best friends who grew up together in Brooklyn, New York. Steve spends most of the Captain America Movieverse chasing Bucky and single-handedly fighting and/or ignoring orders from anyone who tries to stop him, including the US Army, S.H.I.E.L.D., HYDRA, the United Nations, and Iron Man. Of course, even when Bucky is trying to kill Steve, Steve refuses to fight his buddy, his pal, his Bucky, except out of necessity. When Bucky is the Winter Soldier, it is his encounters with Steve that cut through years of brainwashing to trigger his memories of his past life and start him on the path to recovery. Opponents have been known to distract Steve from the task at hand by casually mentioning Bucky.