I guess there is the following difference between ordinal and cardinal numbers:
In physics there is the Zeroth Law of Thermodynamics, a transitivity of temperatures. If A and B have the same temperature, and B and C have the same temperature, then A and C have the same temperature. (A could be melting ice, B expanding mercury, and C bourbon at the correct temperature.) The name for the Law was devised after the names for the three laws of thermodynamics had become standard.