Yes that’s pretty much it
If your parents or some other competent adult has guardianship over you, even if you are an adult, they can have you committed against your will. You need to know if your parents have guardianship over you.
If you are an adult, ie over 18 or 21 depending on your state, and not under guardianship, there are only certain situations where someone can put you in a hospital.
1. If you are in immediate danger of hurting yourself or others. That doesn’t mean saying “I feel empty and am thinking of killing myself.”
Just thinking about it is not a reason to lock you up.
2. Just saying “I hate my father and I’d like to kill him” is not enough to get you locked up. Now, if you say you’ve purchased a gun and plan to kill him when your mother goes grocery shopping today - that’s a little more concrete and might get you in trouble if you insisted this was your plan. If you backed down and said, I don’t really want to kill him, he just makes me mad. That’s different.
3. If you stop eating long enough to endanger your health, you could get committed.
4. If you are cutting yourself badly enough to require stitches, you could get committed.
5. If you try to cut or drop a new baby sister, that would get you committed. But if you say, I hate the new baby because she gets all the attention, that’s not going to get you committed.
Does this answer some of your questions?