Doctoral describes work done as part of the university degree of doctor — the highest research degree, usually a PhD. A doctoral thesis (or doctoral dissertation) is the long piece of writing. A doctoral student is someone doing that degree. A doctoral programme is the course of study. It does not mean “of a medical doctor,” even though we also call a physician Doctor. You can say medical school, but the usual pair is doctoral for the research degree: doctoral research, a doctoral committee. It is an adjective; the name of the degree itself is a doctorate. In everyday talk people often just say PhD.