You cannot compare the two procedures.
The Intersection is a real Geoprocessing thing, stems from Venn-diagram (like Union, Difference). Has an impact on geometry and attributes (both layer attributes inherited) too.
The Clip is a complex method (collecting every touched (in Geomedia) or intersecting (in QGIS, Spatial Query) features in clip polygons, and save them) which does not effect the geometries and the attributes neither.
Touch returns features that touch the defined features in any way—meeting, overlapping, containing, or being contained by. - Working with GeoMedia Professional
The problem is that the GIS language is not standardized.
Look at these images created in QGIS 2.18.9:.
Clipped (line and polygon layers):
Intersected (line and polygon layers):