I had this problem after several years working in ProE / WF.
In UG/NX the philosophy is different.
Usually the intersection between any curve and any surface is one or more points. (It can be an other curve(s) if one or more portion(s) of curve they are included in the surface but this is other case.)
Therefore these intersection(s) are obtained by creating a point / point set using "Intersection" option.
I hope to be clearer in the attached presentation.
It's about the NX CAD software.
There are two situations:
1. Point - To obtain only one intersection point between one surface and one curve.
2. Point Set... - To obtain multiple intersection points between multiple surfaces and multiple curves.
(Menu →Insert→Datum/Point→Point Set…)