a .I came across a woman running in the rain .

b . I came across a woman who is running in the rain.

What is the differences between a and b .
and What situation should i use each ?

Hello

I would say it is a matter of tense confusion with came and is.

I came across a woman running in the rain (came is past tense, you don't say when the woman was running so we assume it was in the past, therefore the sentence works well.)

However,

I came across a woman who is running in the rain (came is past tense and is- is present tense) so you have past and present together causing confusion.

I hope this helps

Hal

If the original poster was looking for the difference between the following, I believe both are fine.

I came across a woman running in the rain.
I came across a woman who was running in the rain.