In most of chemical propulsion engines the product of burning fuel and oxidizer is the propellant; in some cases the ratio between the two is non-ideal, in which case some unburnt fuel acts as propellant as well.
OTOH, in concepts like NTR, or with RTG-powered ion drives, the two concepts - fuel and propellant - are entirely distinct. The nuclear fuel provides energy; the inert propellant is the reaction mass. Another trivial example is from amateur rocketry - the compressed air rocket, where compressed air is the energy carrier, but water expelled by air pressure is the main propellant.
Are there any designs of chemical propulsion though, that would use some low (-to-none) energy density propellant of a very high thermal expansion ratio, together with fuel and oxidizer that when combined provide a lot of thermal energy but not nearly as much exhaust velocity and/or thrust?