to me, very broadly speaking:
anti-civ is a critique of civilization (however one defines "civilization"), which may or may not come from an anarchist perspective (eg, tk). having a critique of civilization does not imply or prescribe a particular way for post-civilized humans to live.
(anarcho)primitivism adds to a critique of civilization a somewhat prescriptive element that implies a particular "correct" way for humans to live - the way humans lived prior to civilization. of course, that can only be surmised from what paleontologists, archaeologists, anthropologists, and other scientists have indicated is "how humans lived" back then. a primary conflict that non-primitivist anti-civ folks i know have with primitivist thought is precisely that prescriptive element, as well as its dependence on authorities (those scientists) and seemingly wholesale acceptance of their body of "evidence".
green anarchy is a broad tendency of anarchist thought, which takes a particular interest in the ecological/environmental impacts of modern (civilized) life, and how it creates and perpetuates institutional hierarchies and oppressions.
a decent starting point for answering this question in more detail might be:
quick edits for clarity.