还是 and 或者 — or in questions and in statements

규칙 还是 goes in a QUESTION offering a choice: 你喝茶还是咖啡？
或者 goes in a STATEMENT: 我喝茶或者咖啡都可以。
Swapping them is a grammatical error, not a matter of style.
还是 has a second sense, still: 他还是没来。