それとも

それとも means "or" between two questions, and asks the listener to pick one. Each option is a question of its own, ending in か, or in a rising tone in casual speech.

それとも or か

Between two nouns, "or" is か, and it works in questions and statements alike. それとも only joins questions. In a statement or a request, it is wrong.

• × 月曜日それとも火曜日に来てください → 月曜日か火曜日に来てください

In writing and in formal notices, "or" in a statement is または.

Only the second option

When the first option is already on the table, a question can start with それとも and offer just the other one.

In casual speech, それか does the same job and can also introduce a suggestion rather than a question.