I told her

Yes.

I said, "I'll call you if I come out tonight."

I said that I would call her if I came out tonight.

what's the difference in meaning if I say

I told her would have called her if I had come out?


it's that the event has no relation to the present?

I meant......I told her would I have called her if I had come out.

I told her I would have called her if I had come out. (You mixed up the would and I but I assume it's a typo. Also, I'd say "gone" instead of "come.")

You didnt't call. She wanted to know why.

Her: You didn't call.
You: I know
Her: But earlier you said that you would call.
You: No, I said that I would call you if I went out. I didn't go out, so I didn

I told her I would call if I go out tonight

.
I told her I would call if I went out tonight