Expressing "to have to" with 不得不 and 不得已
不得不 and 不得已 have both similar and different functions.
The similar meanings
The adverbs 不得不 
and 不得已 emphasize that circumstances are making people do something.
These adverbs are placed before a verb or a verb phrase.
and 不得已 emphasize that circumstances are making people do something.
These adverbs are placed before a verb or a verb phrase. Pay attention
不得已 is stronger than 不得不. This phrase is used to emphasize that a person really doesn’t want to do anything.
Examples
他们不得不半夜离开
They will have to leave in the middle of the night
tāmen bùdébú bànyè líkāi
他不得不去医院接受治疗
He had to go to the hospital for treatment
tā bùdébú qù yīyuàn jiēshòu zhìliáo
他们不得已只能关闭掉这些商店
They had to close these shops
tāmen bùdéyǐ zhǐ néng guānbìdiào zhèxiē shāngdiàn
我不得已而同意了
I had to agree
wǒ bùdéyǐ ér tóngyì le
The adjective 不得已
不得已 also can be an adjective meaning “forced”.
Pay attention
不得不 cannot be an adjective.
Examples
他这样做也是不得已
He has to do so
tā zhèyàng zuò yě shì bùdéyǐ
这些新闻会议是不得已的
Press-conferences were inevitable
zhèxiē xīnwén huìyì shì bùdéyǐ de
不得已 is also used in these set expressions:
万不得已
迫不得已
迫不得已 Examples
迫不得已的话，我总可以开卡车
If I had to, I could drive a truck
pòbùdéyǐ de huà, wǒ zǒng kěyǐ kāi kǎchē
只有在万不得已的情况下才允许使用抗生素
Antibiotics should only be taken as a last resort.
zhǐyǒu zài wànbùdéyǐ de qíngkuàng xià cái yǔnxǔ shǐyòng kàngshēngsù