It feels very different. Depressed people lack the motivation/energy to start exercise, fat people seem more in line with addiction in not being inclined to overcome short term craving for more feed.

While at a certain level of abstraction you can reduce both to A -> !B -> C, that generalization seems to obfuscate specific important differences that impact pathways to treatment. Craving is not the same as lacking energy. Craving, while subversive, energizes, depression does not.