The difference between (1) and (2) is this. For (1), you are looking at an open disk that is properly contained in the open unit disk, but could go right up to the boundary of it. For example, it could be the open disk of radius 1/2 centred at the point z=1/2. But the circle in (2), together with its interior, forms a closed disk. It has to stay strictly away from the boundary of the unit disk. More precisely, it must be contained within the disk (centred at the origin) of radius 1–δ for some δ>0.