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Einstein-Podolsky-Rosen (EPR) steering is an intermediate type of quantumnonlocality which sits between entanglement and Bell nonlocality. A set ofcorrelations is Bell nonlocal if it does not admit a local hidden variable(LHV) model, while it is EPR nonlocal if it does not admit a local hiddenvariable-local hidden state (LHV-LHS) model. It is interesting to know whatstates can generate EPR-nonlocal correlations in the simplest nontrivialscenario, that is, two projective measurements for each party sharing atwo-qubit state. Here we show that a two-qubit state can generate EPR-nonlocalfull correlations (excluding marginal statistics) in this scenario if and onlyif it can generate Bell-nonlocal correlations. If full statistics (includingmarginal statistics) is taken into account, surprisingly, the same scenario canmanifest the simplest one-way steering and the strongest hierarchy betweensteering and Bell nonlocality. To illustrate these intriguing phenomena insimple setups, several concrete examples are discussed in detail, whichfacilitates experimental demonstration. In the course of study, we introducethe concept of restricted LHS models and thereby derive a necessary andsufficient semidefinite-programming criterion to determine the steerability ofany bipartite state under given measurements. Analytical criteria are furtherderived in several scenarios of strong theoretical and experimental interest.

Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario