I don"t know the difference between "I'm sorry (that) S+V" and "I'm sad (that) S+V".
- I'm sorry I went.
- I'm sad I went.
- I'm sorry you're not going to come.
- I'm sad you're not going to come.
Would you explain the difference to me?
"Sad" is an emotion while "sorry" is apologetic; however we can also say we are "sad" as a way to apologize for something.
I'm sorry I forgot your birthday (I apologize that I forgot)
I'm sad I forgot your birthday (I feel bad that I forgot your birthday, by which you should understand that I'm also sorry)
Or we can say we feel "sorry" to imply that some action has us feeling "sad".
I'm sad to hear about the loss of your father. He was such a nice man. (I feel bad that your father died, by which you should understand that I sympathize with you.)
I'm sorry to hear about the loss of your father. He was such a nice man. (I feel bad that your father died, and I'm offering sympathy)
So much depends on the context. However, I think almost every language uses emotions to convey messages. Nor is it limited to just sad/sorry:
I was happy to hear that you graduated from college! (I'm offering congratulations)