"Equivalent" theories represent the very same state of the world; any differences are merely conventional or notational. According to one view of the metaphysics of equivalence - of what equivalence consists in - equivalent theories say the same thing about fundamental reality, understood in a certain fine-grained way. According a second view, which I call "quotienting" (short for "quotienting-out conventional content by hand"), theories may be equivalent even when we cannot state, in an intrinsic or "artifact-free" way, the content that the theories have in common. These two views are in a sense the extremes. The first view (which I accept) leads to uncomfortable conclusions about the kinds of questions that are genuine (e.g., whether negation and conjunction, as opposed to negation and disjunction, form the metaphysically correct basis for propositional logic). The second is dizzying, but sheds light on various otherwise perplexing viewpoints in metaphysics, philosophy of physics, and philosophy of mathematics.