Conductors, insulators, and semi-conductors all have physical definitions relating to how their valence electrons behave. But from the simpler electrical point of view, the difference between conductors and insulators is simply their conductance/resistance. Insulators conduct very poorly, conductors conduct well. You can make a conductor (say, a metal wire) conduct poorly (by making it very thin or by heating it). It's more difficult to make an insulator conduct better.
Semiconductors are a very different beast. Their conductance depends on many more factors than mentioned here and are out of the scope of the question.
But to make a long story short, nearly everything conducts, but how much it conducts can vary by many orders of magnitude.