Mildew is essentially the precursor to mould, and isn't as dangerous. It will first show itself as a patch of white/yellow spots before quickly turning brown or black. It's a surface mould, so it can easily be removed.
Mould, on the other hand, is black or green and is a sign of a much larger infestation. It can penetrate below the surface of the affected area and cause serious damage if left untreated for a long time.