It is often indeterminate what function a given computational system computes. This phenomenon has been referred to as "computational indeterminacy"or "multiplicity of computations."In this paper, we argue that what has typically been considered and referred to as the (unique) challenge of computational indeterminacy in fact subsumes two distinct phenomena, which are typically bundled together and should be teased apart. One kind of indeterminacy concerns a functional (or formal) characterization of the system's relevant behavior (briefly: how its physical states are grouped together and corresponded to abstract states). Another kind concerns the manner in which the abstract (or computational) states are interpreted (briefly: what function the system computes). We discuss the similarities and differences between the two kinds of computational indeterminacy, their implications for certain accounts of "computational individuation"in the literature, and their relevance to different levels of description within the computational system. We also examine the inter-relationships between our proposed accounts of the two kinds of indeterminacy and the main accounts of "computational implementation."