还是 vs 或者 (or: question vs statement)

"Or" — question or statement?

• Both or / still还是hái shì and or或者huò zhě mean "or" — but they don't mix.
• or / still还是hái shì = "or" in a question; or或者huò zhě = "or" in a statement.
• Pick by whether you're asking or telling.

or / still还是hái shì → questions

• A choice question uses or / still还是hái shì.

you你nǐdrink喝hētea茶cháor还是hái shìcoffee咖啡kā fēi？

• you你nǐto drink tea喝茶hē cháor / still还是hái shìcoffee (loanword)咖啡kā fēi？ = "tea or coffee?"

or或者huò zhě → statements

• A statement of options uses or或者huò zhě.

tea茶cháor或者huò zhěcoffee咖啡kā fēiboth都dōufine行xíng。

• tea茶cháor或者huò zhěcoffee (loanword)咖啡kā fēi都行dōu xíng = "tea or coffee, either is fine."

Recap

Read the full reference: HSK 3 grammar — Comparing conjunctions.