The authors provide an equivalence theorem for certain linear combinations of Bernstein-Kantorovich operators which characterizes the pointwise order of approximation of a continuous function \(f\in C[0,1]\) in terms of the \(t\)-order of the Ditzian-Totik-type modulus of smoothness \(\omega^{2 r}_{\varphi^\lambda}(t)\). The theorem unifies some order of approximation results characterized in terms of classical and Ditzian-Totik moduli of smoothness.