The hierarchy of nonlocality and entanglement in multipartite systems is one of the fundamental problems in quantum physics. Existing studies on this topic to date were limited to the entanglement classification according to the numbers of particles enrolled. Equivalence under stochastic local operations and classical communication provides a more detailed classification, e. g. the genuine three-qubit entanglement being divided into W and GHZ classes. We construct two families of local models for the three-qubit Greenberger-Horne-Zeilinger (GHZ)-symmetric states, whose entanglement classes have a complete description. The key technology of construction the local models in this work is the GHZ symmetrization on tripartite extensions of the optimal local-hidden-state models for Bell diagonal states. Our models show that entanglement and nonlocality are inequivalent for all the entanglement classes (biseparable, W, and GHZ) in three-qubit systems.
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