The first part of the Marvel Cinematic Universe has been titled the Infinity Saga for some time now, aptly named as the overarching story revolved around introducing the Infinity Stones to the continuity just for Thanos to swipe and use them to carry out cosmic genocide. In the comics, the Mad Titan gave his quest a different title, one that is far more fitting of his beliefs: Infinity Crusade.
While Thanos' drive in the movies was based on what he believed to be universal salvation, his motivation in the comics is different. Thanos worships Death far more than anything else. The exact nature of this worship is something that Thanos fans can't agree on, but the general consensus is that everything Thanos does is in Death's name. She did bring him back from the dead to carry out her will, after all.
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This act began what Thanos personally sees as his infinity crusade (not to be confused with the Infinity Crusade storyline), referred to in 2016's Thanos #14 by Donny Cates and Geoff Shaw. It was a campaign full of death and chaos in pursuit of artifacts that would allow him to right what Death has told him is wrong with the universe. According to her, there are more things that are alive than have ever died, and so to please Death, Thanos devoted himself to her, and went on to balance the scales. Although, the lives lost were ultimately brought back and the Mad Titan defeated, his mark was left on the Marvel Universe and is still felt to this day. As a matter of fact, Thanos' crusade is why the symbiote Carnage was born.
Thanos' quest in the comics could also be referred to as the Infinity Saga, but saga denotes a series of significant events
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