So, as was noted by @BlueBarren, both the Wii U hasand the Switch have the ability to have multiple profiles. Some of us have always just gone along with a singular profile with no need to have any additional profiles...
If you want to have more than one game state saved in Breath of the Wild, we can simply make a profile for each player that would like to maintain their game state and play it as that user / profile!
Good to know and thanks!