或者huò zhě and 还是hái shì both can act as the conjunction ‘or’ in the sentence to provide possible options or choices. However, there are some differences between them.
还是 is used when you need to make a question.
nǐ xiǎng chī xīguā hái shì píng guǒ
e.g. 你想吃西瓜还是苹果？Would you like to have Watermelon or apple?
There is no need to add any question particles, however you can add it to add a bit more flavour (put emphasis to your tones) in the sentence,
nǐ xiǎng chī xī guā ne? Hái shì píng guǒ ne?
On the other hand, if you want to use 或者 in a sentence, you will need to add question particles,
nǐ xiǎng chī xī guā huò zhě píng guǒ ma
e.g. 你想吃西瓜或者苹果吗？ Would you like to have watermelon or possibly apple (or other fruit)?
The meanings are also slightly different between these two sentences. With the 还是question, the person only gives you the choices between watermelon and apple， the options are limited. With the 或者 question, the person is asking you whether you would like to have watermelon or apple, or maybe other fruits. The choices are unlimited.
The first question can be used in situations, for example, when there are guests at home but you only have watermelon and apple available to offer. The second question can be used, for example, when you are in a supermarket, and you decide to call your mother to ask whether she wants you to bring any fruit home.
For both questions, you can answer with,
xī guā huò (zhě) píng guǒ dōu kě yǐ.
西瓜或（者）苹果都可以。 Watermelon or apple both okay.
Other examples can be,
if you and your friend are planning to go on a trip together, you are limiting the choices to Spain and Portugal, you can say,
nǐ xiǎng qù xī bān yá hái shì pú táo yá
你想去西班牙还是葡萄牙？ Would you prefer to go to Spain or Portugal?
However, if you and you friend haven’t talk about going on a trip together, however you want to suggest about a trip,
nǐ xiǎng qù xī bān yá huò zhě pú táo yá ma
Do you want to go somewhere possibly Spain or Portugal (or some other places)?
If you are being rubbed, the criminal got his knief out and ask you,
nǐ yào qián hái shì yào mìng
你要钱还是要命？ You want money or your life?
In such case, 还是 is the appropriate word, because if the sentence changes to，
nǐ yào qián huò zhě yào mìng ma
你要钱或者要命吗？ Would you possibly want some money and life?
It sounds more like the criminal is offering money and a life.
还是 also can be used in a statement provide that you are not sure about that matter, for example,
if you want to buy a designer bag and not sure if it’s real or fake, you say,
zhè bāo bù zhī dào shì zhēn de hái shì jiǎ de
这包不知道是真的还是假的。 Don’t know this bag is real or fake.
On the other hand, if you don’t care if it’s real or not you just going to buy it, then you can use both 还是 and 或者，
bù guǎn zhè bāo shì zhēn de hái shì jiǎ de, wǒ dōu huì mǎi.
不管这包是真的还是假的，我都会买。No matter this bag is real or fake, I am going to buy it.
bù guǎn zhè bāo shì zhēn de huò zhě shì jiǎ de, wǒ dōu huì mǎi.
不管这包是真的或者是假的，我都会买。No matter this bag is real or fake, I am going to buy it.
During exams, you are most likely to come across questions asking you to choose between A, B or C, or between true or false,
if the question is actually in a question format, it will be translated as
zhè dào tí de dá’àn shì A,B hái shì C
这道题的答案是 A、B 还是C？ Is the answer to the question A, B or C?
zhè dào tí shì duì hái shì cuò
这道题是对还是错？Is the answer true or false?
On the other hand, if the question is written in a statement, it will be translated as,
qǐng xuǎn zé A, B huò (zhě) C
请选择 A， B 或（者） C。
qǐng xuǎn zé duì huò (zhě) cuò