Is market failure the same allocative inefficiency?
In this context 'market' usually means some allocation mechanism. For example free market, or a market where someone has monopoly power. Allocation of goods and resources can be done in other ways: e.g. you can divide all resources evenly among production processes and all goods evenly between consumers. This will generally result in allocative inefficiency (were all production processes equally important and efficient?). But it is not market failure because there was no market, just an allocator/social planner.