Thermal resistance vs thermal impedance

The basics are simple. Thermal resistance is K/W (note that both are capitalized, because the unit names are proper names). Resistance and impedance are essentially the same thing, unlike electrical resistance and impedance. Conductivity is the inverse of resistance in W/K. But, unlike the nice simple electrical schematics people often come with for thermal networks, thermal systems are area and thickness related; the larger the area, the lower the thermal resistance, and the thinner the material the lower the thermal resistance. Thus, K*m/W is thermal resistivity, and requires multiplication by thickness/area to get thermal resistance. K*m^2/W is apparently called thermal insulance, which is the thermal resistance of a unit area of, typically, an insulation material

While it is very common to use W/(mK) for thermal conductivity, you have to understand that this is a contraction of W/[(m2)(K/m)]. It seems to be simple arithmetic to simplify and cancel meters by meter. But in this equation meters in the x and y directions are used to calculate surface area, and meter in the z direction represents thickness. These are not the same physical quantities and therefore should not be canceled out. Apples versus oranges. You must understand this when doing calculations.

Thermal resistance and impedance are not material properties, but apply to specific devices or structures. They are usually used to mean the same thing, but may have definitions that vary by industry.

Thermal diffusivity is thermal conductivity divided by heat capacity. This is used in dynamic heat transfer calculations as opposed to static or equilibrium calculations. The rate at which a temperature change propagates through a material depends on the diffusivity.

Thermal impedance could be used to mean the inverse of thermal diffusivity. In the electrical world impedance is a function of resistance, capacitance, and inductance. Heat capacity behaves similarly to capacitance and inductance.