  Classifying states which exhibiting different statistical correlations is
among the most important problems in quantum information science and quantum
many-body physics. In bipartite case, there is a clear hierarchy of states with
different correlations: total correlation (T) $\supsetneq$ discord (D)
$\supsetneq$ entanglement (E) $\supsetneq$ steering (S) $\supsetneq$
Bell~nonlocality (NL). However, very little is known about genuine multipartite
correlations (GM$\mathcal{C}$) for both conceptual and technical difficulties.
In this work, we show that, for any $N$-partite qudit states, there also exist
such a hierarchy: genuine multipartite total correlations (GMT) $\supseteq$
genuine multipartite discord (GMD) $\supseteq$ genuine multipartite
entanglement (GME) $\supseteq$ genuine multipartite steering (GMS) $\supseteq$
genuine multipartite nonlocality (GMNL). Furthermore, by constructing precise
states, we show that GMT, GME and GMS are inequivalent with each other, thus
GMT $\supsetneq$ GME $\supsetneq$ GMS.
