或(者) and 還是 can be translated as “or” in English, but there’s a distinction between these two words.
還是 typically appears in a question which offers choices, while 或者 is normally used in a statement.
請你給我一杯茶或(者)咖啡。
qǐng nǐ gěi wǒ yī bēi chá huò ( zhě ) kā fēi
Please give me (either) a cup of tea or a cup of coffee.
你要汽水還是茶？
nǐ yào qì shuǐ huán shì chá
Do you want soda or tea?
When 或者 is used in a question, it is an affirmative-negative question or a question with the sentence-final particle ma (嗎).
我想喝一點飲料，有沒有茶或者汽水? (=有茶或者汽水嗎?)
wǒ xiǎng hē yī diǎn yǐn liào ， yǒu méi yǒu chá huò zhě qì shuǐ
I want to drink something. Is there tea or soda?
Reference: YUFA! A Practical Guide to Mandarin Chinese Grammar
