What is the main difference between Consumption CAPM (CCAPM) and the Intertemporal CAPM?

As per my lecture notes the C-CAPM explains that an asset which has a higher payoff in low consumption periods will be priced higher than an asset that only yields return during periods of high consumption. Therefore showing that rational investors do not just care about expected returns but that using such assets to hedge against periods of economic downturn are invaluable.

My question is however, I have been given a task to critically evaluate asset pricing models with reference to theoretical and empirical research. Two of the models include Consumption CAPM and Intertemporal CAPM - I am struggling to differentiate between them as they both seem to be based on marginal utility of wealth and consumption assets. Can you explain this?