What is the difference between hydrogen chloride and hydrochloric acid?
Hydrogen chloride is a gas. It is the molecule made up of a hydrogen and a chlorine atom bonded by a single bond. It comes in gas cylinders for use in chemistry.

Hydrochloric acid is a solution (no, not to your problem of a stubborn teacher). It is composed of water molecules and hydrogen chloride molecules. In terms of mass percentage, concentrated hydrochloric acid is often $37~\%\ \ce{HCl}$ in water. It comes in glass bottles (often brown glass for ease of bottle use; the chemical company does not have to distinguish between compounds that can live in clear bottles and those that must live in brown ones) for use in chemistry.

Hydrogen chloride can also be dissolved in other solvents such as ether. In this case too, it may be termed hydrochloric acid, although a specification of the solvent should be added.

Whether or not either of the two names is a misnomer depends on what you are addressing. Using hydrogen chloride for the liquid solution is as wrong as using hydrochloric acid for the gas.