By applying properly the concept of twist symmetry to the gauge invariant theories, we arrive at the conclusion that previously proposed in the literature noncommutative gauge theories, with the use of ⋆-product, are the correct ones, which possess the twisted Poincaré symmetry. At the same time, a recent approach to twisted gauge transformations is in contradiction with the very concept of gauge fields arising as a consequence of local internal symmetry. Detailed explanations of this fact as well as the origin of the discrepancy between the two approaches are presented.