Consider a simple network consisting of a source with some internal impedance, and the DYn-transformer. The source is connected to the D-side.
When there is a line to earth fault on the secondary (Y) side, current flows in one secondary winding only. On the primary side, current flows also in one winding. One phase of the source feeds current to (or from) one primary winding only.
In the case of a three phase fault, there is current in all windings of the transformer. Each phase of the source feeds current to (or from) two primary windings, not one, as in the case of the earth fault. Thus, due to the internal impedance of the source, the current in one winding must be smaller than in the case of the line to earth fault. As a consequence, the fault current is also smaller.