In terms of band theory, what is the difference

In terms of band theory, what is the difference
(i) between a conductor and an insulator?
(ii) between a conductor and a semiconductor?

(i) In a conductor, the energy gap between the valence band
and the conduction band is very small or there is an overlapping between conduction and valence bands. In an insulator, this gap is very large.
(ii) If the energy gap between valence and conduction bands is
small, then it is a semiconductor. But if the gap is very small then there is an overlapping between the two bands, it is a conductor