  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 $\star$-product, are
the correct ones, which possess the twisted Poincar\'e 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 {\it local}
internal symmetry. Detailed explanations of this fact as well as the origin of
the discrepancy between the two approaches are presented.
