WARNING: The following article contains spoilers for Marvel's Black Widow, now playing in theaters and on Disney+ Premier Access.
The relationship between Black Widow and the Red Guardian was a key aspect of the Marvel Cinematic Universe film. However, the need to update the Red Guardian for the purposes of continuity also came a major change in the dynamic of their original relationship.
The movie portrayed Alexei Shostakov as a father figure to the young Natasha Romanov. But in the comics, Alexei was Natasha's husband, not her father. However, both still had a hand in the events that led to Natasha becoming the Black Widow.
The Alexei Shostakov in Black Widow is portrayed very much like he is in comics, a patriot super soldier created to act as a counterbalance to Captain America. Unlike the Alexei of the comics however, this version never met Steve Rogers. The Avenger he did meet and partially raise was Natasha. When she was very young, Natasha was assigned to work with Alexei as part of a fake family to maintain deep cover while in America. Though essentially a sham, the three years spent undercover were among the happiest years of Natasha's life, giving her a brief taste of what normality felt like.
Sadly, the mission came to an end and Natasha was returned to the Red Room where she was trained to be the perfect assassin. Her relationship with Alexei soured after that, as he had done nothing to prevent her return to her highly abusive handlers, despite her adamant protests about returning to the Red Room. Fate would force the two to work together again when Natasha needed to find the Red Room in order to destroy it. But she needed a lead and the only person she could think of was Alexei, who she broke out of prison. Interestingly this is similar to when she broke him out of prison in the comics as well.
The relationship between Black Widow and Red Guardian was decidedly different than what appeared in the comics. On the printed page, Alexei Shostakov was actually Natasha Romanov's husband. He was a premier pilot for Russia and because of this, he was selected to become the second Red Guardian. To do so, Alexei faked his death, abandoning his wife to become Russia's super-soldier.
The resulting grief from believing her husband was dead led Natasha to become the Black Widow. She ended up allying herself with the very person Alexei was trained to oppose, putting the two on opposing sides of a political conflict. But, much like the movie, Alexei's love for Natasha won out over any standing loyalties to his country. He sacrificed his life to keep her safe, forsaking the very reason he had left her in the first place.