Who refers to people (and animals with a name!).
That may refer to people, animals (without a name), groups, or things.
1. Was it Sally who organised the surprise party for Michael? (that is also acceptable.)
2. The man who wanted to talk to you left an hour ago. (that is also acceptable.)
3. I don’t want to go to any amusement park that costs more than €40.
4. Thomas is the president of the association that looks after injured wild animals.
Please note: To me, using ‘that’ for a person makes person seem less human!