If a black body is simply an element, why would it, at a given temperature, emit electromagnetic radiation as a continuous spectrum, when an element is said to emit light in specific frequencies?

When you look at the Intensity vs wavelength plots of a black body at a given temperature, it's a continuous curve. A black body is still an element, is it not? Why would it emit radiation continuously as opposed to discretely? I realize that some wavelengths occur in greater amounts, but it's still continuous. This makes no sense to me, especially since black body radiation is usually presented in trying to understand that energy comes in the form of discrete packets.