Compensation wire is wire that is used in a thermocouple from the point of sensing to the point of cold junction compensation (cjc end) where the signal is measured.
Extension grade wire is only used to extend a thermocouple signal from a probe back to the instrument reading the signal. The extension grade wire typically will have a lower ambient temperature limit in which the wire may be used. Namely, it may pass a signal representing a higher temperature as received from the probe, but the wire physically may not be exposed to higher temperatures. Thermocouple wire may be used as extension wire, but extension grade wire may not be used in the sensing point (or probe part) of the thermocouple. Part numbers for extension wire typically begin with an "EX" prefix.