There were five types, depending on the type of dragon egg. In Krynn (Dragonlance), draconians (the first half-dragons/Dragonborn in D&D) were the result of a magical corruption of metallic dragon eggs. So no “dragon sex” and the dragon would always be the father (because the human/elf, whatever is giving birth), and only dragons that can take a humanoid form without a spell could do so, making most of the metallic dragon offspring.
Well traditionally half-dragons would have been the offspring of a dragon in humanoid form.