Yes, HSRs share the same tags wih conventional railways.
Some systems like the French TGV have extensive networks of railway lines used only by HSRs. But some don't, for example the Polish EIP services share all its rail with other trains (and mostly runs on tracks degsined for slower trains). Both HSRs and conventional railways are compatibile with each other unless there are other technicalities involved (gauge, voltage etc.)
HSR tracks have bigger radiuses of curves. besides that - not much.
There should be added that if there is a railway, let's say in the city which has four tracks or more one pair of tracks should be exclusive for HSR especially when some minor stops should be missed by the fast trains, even if in the whole country the tracks are shared.