Systemic & Emergent Games
Systemic games are games that are created such that all their individual systems can reach out and influence one another. A good example of this design philosophy is the rain mechanic in Breath of the Wild. When it rains in Breath of the Wild, the whole game world is affected. Surfaces are harder to climb, and visibility is affected, but Link's footsteps are muffled so sneaking around is easier.
Systemic games are unique because they offer a level of experimentation and player control than that of other more traditional game designs. The following video from The Game Maker's Toolkit provides an quick look at systemic games.
In addition to systemic games there are emergent games, these are games that allows the player to create solutions or elements that the designer never intended. The key thing to keep in mind is that in order for a game to feature emergent gameplay, what's been created by the designer must have enough adaptability to be transformed by the player.
Sandbox Games
Sandbox games provide the player with a great degree of creativity to interact with, usually without any predetermined goal, or alternatively with a goal that the player sets for themselves. A sandbox will have a combination of game mechanics and player freedom that can lead to emergent gameplay.
The following video from The Game Overanalyser, helps to provide a taxonomy for different types of emergence, strategic, systemic and narrative emergence, and try to navigate our understanding of them all.