They are all terms that eventually refer to the same thing.

The electrical load of the train i.e., the power required to run all the lights, fans, A/C, pantry equipment and basically everything in the coaches, is called 'Hotel Load'.

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load can be supplied by EOGs or directly from the locomotive.

Since the locomotive is at the 'head' of a train, the generation of power through the locomotive is called 'Head-On Generation' (HOG) or 'Head end Power' (HEP) [Both terms basically mean the same].

The power generated through HOG (or HEP) is used for meeting the 'Hotel Load'. The couplers used for supplying this power are referred to as 'Hotel Load couplers' (HLC) but there is nothing wrong in simply referring to them as HOG couplers.