Well... This is right... but not exactly right. Grammatically in phrases like "A is B" in literary Russian, B can be either short form adjective or noun, but not full form adjective. When B looks like a full form adjective, in fact it is an adjectival noun.
So "Он болен"="He is sick", "Он - больной"="He is a sick person" or "He is a patient"
Often it has effect described as "short term VS permanent", but not always.