CP is Tucker with a superdiagonal core

Both models approximate an N-way tensor with one factor matrix per mode. They differ only in how the columns of those matrices may combine:

CP:     x_ijk ≈ Σ_r a_ir · b_jr · c_kr
Tucker: x_ijk ≈ Σ_pqs g_pqs · u_ip · v_jq · w_ks

In CP, column r of one factor meets only column r of the others. In Tucker, a core tensor lets every column meet every other column, and the core entry g_pqs says how much that meeting contributes.

Set every Rₙ = R and zero every core entry except g_rr…r, and the Tucker sum collapses to the CP sum. CP is Tucker with a superdiagonal core — and storage, identifiability and expressiveness all follow from that one difference.