You can set a surface so that all creation tools (such as the curve drawing tools) are locked on to the surface. This does not affect actions (such as the create primitives commands).
To snap creation tools to the selected surface
While the Make live icon is on, creation tools snap to the surface. Click the icon again to stop snapping to the surface.
To snap creation tools to a plane
While the Make live icon is on, creation tools snap to the surface. Click the icon again to stop snapping to the surface.