As is often the case, the answer to this is actually slightly context-dependent. For many everyday purposes, the answer of Cort Ammon that it is all a matter of degree is correct.
However, one other context worth mentioning is when condensed matter physicists speak of whether a particular state of matter is a "conducting" (or "metallic") state or an "insulating" state. In this case there is a precise distinction: a conducting state is one that is gapless, meaning that as the size of the material tends towards infinity (the so-called "thermodynamic limit"), the energy difference between the ground and first excited state of the material also tends towards zero*. One can use this to classify various states of matter unambiguously and study transitions between them.
For many typical materials the classification according to this scheme will line up with the "everyday" classification, but in principle there could be exceptions. One could imagine, for example, a material that has a persistent gap but that gap is much smaller than the scale of thermal excitations, so at room temperature it is effectively conducting.
See also this blog post for some nice entry-level details on this classification.
*slightly more precisely, the spectrum near the ground state becomes continuous. The distinction becomes important in Anderson insulators, which are insulators but have a pointlike discrete energy spectrum.