If "it's hurt," that means that it is or has been hurt: it is injured or in pain. "A bird flew into the closed window, and I thinks it's hurt."

If "it hurts," then the speaker is in pain, and it is the body part where the pain is. "I stubbed my toe and it hurts."

"It's hurt by them" and "It hurts someone"  , to feel the differences of them

I think the biggest difference is passive and active <strike></strike>