Continuing the study of the relationship between $TC^0$,
$AC^0$ and arithmetic circuits, started by Agrawal et al.
(IEEE Conference on Computational Complexity'97),
we answer a few questions left open in this
paper. Our main result is that the classes Diff$AC^0$ and
Gap$AC^0$ coincide, under poly-time, log-space, or log-time
uniformity. From that we can derive that under logspace
uniformity, the following equalities hold:
\[C_=AC^0=PAC^0=TC^0.\]