It has stopped raining/the rain has stopped

Hi,
I want to know if the phrase ‘the rain has stopped’ is correct, because it was my translation from an Arabic phrase but the answer I was given was ‘It has stopped raining’.

Could my answer be correct? And if so, is there any difference between the 2 phrases?
.
.
.
Another question:
Is it correct to say ‘birth date’? … Because again that was my translation but the answer I was given was ‘date of birth’. Even though I know ‘date of birth’ is correct but it happened to write ‘birth date’.

.
.

Thanks.

Your answer could be correct, but perhaps the context indicated differently.
There’s no difference in meaning.

‘Birth date’ is possible too, but again possibly the context indicated otherwise.

Thanks for the response Ma’am,

You mean that both words could be used depending on the context?
If so, may you give me an example for each word to know the difference of contexts?

Thanks.