Fast moving coronal mass ejections (CMEs) travelling in interplanetary (IP) space generally drive shocks ahead of their leading edges. Such travelling IP structures may encounter the Earth’s magnetic environment from their central, intermediate or near-end locations. In these three situations, the Earth and its magnetosphere region will be engulfed in different interplanetary plasma and field conditions. Thus, the geomagnetic disturbances generated in three distinct types of solar-terrestrial interactions are expected to be different, not only in their intensity but also in their temporal behavior and recovery characteristics. In this work, we study the effects of such distinct crossings of the IP structures on the characteristic properties of resulting geomagnetic disturbances. We find differences in the Storm Sudden Commencement (SSC) magnitudes, Geomagnetic Strom (GS) amplitudes, and rates at which Dst changes during main and recovery phases in three impact conditions. We analyze simultaneous changes in geomagnetic activity and interplanetary plasma/field parameters in three different situations when the IP structure encounters the Earth from central, intermediate and the near-end portions of its extended structure. We observe that CME-associated IP shocks are most geoeffective when they cross the magnetosphere through their central part. The GS generated during such crossings are likely to recover at a faster rate during their recovery phase, as compared to the GS generated during intermediate or near-end crossings.