North America is a name given to a continent in the seven continent geographic model, which is the one generally used in the English-speaking world. Some other languages and cultures use other models with different numbers and different definitions of continents. I don't know which one you use.
North America is a name in that system. Everything above Panama, including Panama, is North America.
north America is a description identifying the northern section of some place called America. It's not a name, like North America is. We would be more likely to describe it as northern America if that's what we meant.