Aloy and Link Face Robotic Enemies Built By Their Predecessors
While one game is clearly going for more of a futuristic, sci-fi thing, and the other is going for fantasy, they both are preceded by events where the machines that were built by humans (Hylians in Breath of the Wild) went wild and killed nearly everyone, forcing the survivors into corners of the world.
In Horizon Zero Dawn, the humans built a bunch of robots for who knows what reason. Unfortunately, around the time when the company behind their development started to move into the weapon side of things, a glitch appeared in the system that caused the machines to start devouring all of the resources. This basically caused the apocalypse, and now humanity is struggling to put the pieces back together. But now, machines spewing the machines are acting up again after being corrupted by red blasts of corruption, and they are part of the obstacles Aloy must overcome to uncover history and save the world.
In Breath of the Wild, the Guardians didn’t immediately take over and kill everyone (thank goodness for that). They were built thousands of years before the events of the game, but 100 years before Link wakes up, Ganon took them over and turned them against Hyrule. You know what Ganon used to turn them? Huge, reddish/purplish blasts of corruption. Two completely different universes that use the same method to turn machines into homicidal pieces of equipment.