Should my brother see a psychiatrist or a psychologist?

What is the difference between a psychologist and a psychiatrist? And which should my brother see? Do they take health insurance?

My brother is a freshman in high school and he is still afraid of sleeping alone. He often does my sisters chores so she will sleep in his room. My mom doesn’t allow him to watch scary movies because of how afraid he gets but when he does watch them he ends up in my parents bedroom. He even gets really mad if someone jumps out and scares him. He is convinced that our house (that we built and have been in for all of his life) is haunted even though the rest of do not think so. He is tired of always being afraid and really wants to talk to someone and get help. However, he will not talk to a school counselor or our pastor because he is to embarrassed to talk to someone he knows. Any suggestions?