Ending turns and phases

Some cards forcibly end the turn. Magic R&D use the slang term manipulate time for this ability.

It is a primary in blue and flavored as time manipulation (Time Stop, Day's Undoing) Red has done it once with a "lose at end of next turn" rider (Glorious End).

It also appears on the artifact Sundial of the Infinite.

Mandate of Peace is the only card that can end a phase.

Rules

From the Comprehensive Rules (June 7, 2024—Modern Horizons 3)

• 721. Ending Turns and Phases
  • 721.1. Some cards end the turn. When an effect ends the turn, follow these steps in order, as they differ from the normal process for resolving spells and abilities (see rule 608, “Resolving Spells and Abilities”).
    • 721.1a If there are any triggered abilities that triggered before this process began but haven’t been put onto the stack yet, those abilities cease to exist. They won’t be put onto the stack. This rule does not apply to abilities that trigger during this process (see rule 721.1f).
    • 721.1b Exile every object on the stack, including the object that’s resolving. All objects not on the battlefield or in the command zone that aren’t represented by cards will cease to exist the next time state-based actions are checked (see rule 704, “State-Based Actions”).
    • 721.1c Check state-based actions. No player gets priority, and no triggered abilities are put onto the stack.
    • 721.1d The current phase and/or step ends. If this happens during combat, remove all creatures and planeswalkers from combat. The game skips straight to the cleanup step; skip any phases or steps between this phase or step and the cleanup step. If an effect ends the turn during the cleanup step, a new cleanup step begins.
    • 721.1e Even though the turn ends, “at the beginning of the end step” triggered abilities don’t trigger because the end step is skipped.
    • 721.1f No player gets priority during this process, so triggered abilities are not put onto the stack. If any triggered abilities have triggered since this process began, those abilities are put onto the stack during the cleanup step, then the active player gets priority and players can cast spells and activate abilities. Then there will be another cleanup step before the turn finally ends. If no triggered abilities have triggered during this process, no player gets priority during the cleanup step. See rule 514, “Cleanup Step.”
  • 721.2. One card (Mandate of Peace) ends the combat phase. When an effect ends the combat phase, follow these steps in order, as they differ from the normal process for resolving spells and abilities (see rule 608, “Resolving Spells and Abilities”).
    • 721.2a If there are any triggered abilities that triggered before this process began but haven’t been put onto the stack yet, those abilities cease to exist. They won’t be put onto the stack. This rule does not apply to abilities that trigger during this process (see rule 721.2f).
    • 721.2b Exile every object on the stack, including the object that’s resolving. All objects not on the battlefield or in the command zone that aren’t represented by cards will cease to exist the next time state-based actions are checked (see rule 704, “State-Based Actions”).
    • 721.2c Check state-based actions. No player gets priority, and no triggered abilities are put onto the stack.
    • 721.2d The current combat phase ends. Remove all creatures and planeswalkers from combat. Effects that last “until end of combat” expire. The game skips straight to the next phase, usually the postcombat main phase; skip any steps between this step and that phase.
    • 721.2e Even though the combat phase ends, “at end of combat” triggered abilities don’t trigger because the end of combat step is skipped.
    • 721.2f No player gets priority during this process, so triggered abilities are not put onto the stack. If any triggered abilities have triggered since this process began, those abilities are put onto the stack during the following phase, then the active player gets priority and players can cast spells and activate abilities.
    • 721.2g If an effect attempts to end the combat phase at any time that’s not a combat phase, nothing happens.

From the glossary of the Comprehensive Rules (June 7, 2024—Modern Horizons 3)

End the Turn

To “end the turn” as the result of an effect is to perform an expedited process that skips nearly everything else that would happen that turn. See rule 721, “Ending Turns and Phases.”