Two thermodynamic systems are in thermal contact when their boundary permits heat transfer. They need not already be in thermal equilibrium: contact between unequal temperatures is precisely how equilibration can begin. Contact specifies an allowed exchange; equilibrium specifies its balance.
The common boundary between two conducting materials in a thermal interface problem. Perfect thermal contact imposes continuity of temperature and of normal heat flux.
A diathermal wall permits heat transfer. For a clean zeroth law of thermodynamics comparison, idealize it as rigid and impermeable, excluding boundary work and matter transfer. A thin metal partition approximates this arrangement.[ref]
4 Classical Thermodynamics. §4.1, printed p. 109: rigid, particle-impermeable diathermal walls and the thin-metal example
An adiabatic wall prevents heat transfer. Two bodies at and can remain separated by a rigid adiabatic wall with no heat transfer, although they are not in thermal equilibrium with each other. An adiabatic boundary alone need not make a system an isolated system: a moving insulated piston can still transmit work. Isolation additionally excludes matter transfer and every energy exchange.
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Thermal contact refers to the interaction at the interface between two materials that are in thermal contact with each other. This contact affects the transfer of heat between the materials. When two surfaces are brought together, they do not have perfect contact due to microscopic irregularities, leading to gaps and variations in contact area. These irregularities influence thermal conductivity and the overall thermal resistance at the interface.