The difference between 对不起 and 不好意思
对不起 and 不好意思 can both be translated as “sorry”. Let's see the difference between them.
不好意思
We use 不好意思 
mostly in colloquial speech when we feel uncomfortable about the mistake.
mostly in colloquial speech when we feel uncomfortable about the mistake.
Examples
不好意思，我没见到你的短信
Sorry, I didn't see your message
bù hǎoyìsi, wǒ méi jiàn dào nǐ de duǎnxìn
不好意思，我不是特意的
Sorry, I didn't mean to
bù hǎoyìsi, wǒ bùshì tèyì de
We can also use 不好意思 to start a conversation with a stranger when we want to ask them something:
Examples
不好意思，你能告诉我"友谊"宾馆怎么走吗？
Excuse me, can you tell me the way to the "Friendship" hotel?
bù hǎoyìsi, nǐ néng gàosu wǒ yǒuyì bīnguǎn zěnme zǒu ma
Sometimes 不好意思 can also mean “embarrassed”, “ashamed”.
It can be used either in a set expression:
感到不好意思
Or as an adverbial modifier: “to do something shyly”. Sometimes we can also use the particle 地 after 不好意思 and before the following verb denoting action.
Or as an adverbial modifier: “to do something shyly”. Sometimes we can also use the particle 地 after 不好意思 and before the following verb denoting action.Examples
她不好意思地回答
She replied shyly
tā bù hǎoyìsi de huídá
我真不好意思说我向她撒了谎
I'm embarrassed to say I lied to her
wǒ zhēn bù hǎoyìsi shuō wǒ xiàng tā sā le huǎng
对不起
We use 对不起 in a more formal way. It can be used either in colloquial speech or written language. However the emotional coloring is stronger and the speaker feels more guilty:
in a more formal way. It can be used either in colloquial speech or written language. However the emotional coloring is stronger and the speaker feels more guilty:Examples
对不起，我失态了
Sorry, I lost my temper
duìbuqǐ, wǒ shītài le
对不起，是我错了
Sorry, it was my fault
duìbuqǐ, shì wǒ cuò le
We can use adverbs of degree before 对不起 and 不好意思:
很
实在
真
非常
实在
真
非常 Examples
真对不起，我忘了你的生日了
I'm really sorry, I forgot about your birthday
zhēn duìbuqǐ, wǒ wàng le nǐ de shēngrì le
Pay attention
To sum it up:
不好意思 is used in colloquial speech. We use it to apologize for a small fault or to express embarrassment.
对不起 is used both in colloquial speech and in writing. We use it to apologize for small faults or for more serious mistakes.