You were close. Essential is to know that defining a stroke color and defining a fill color is what determines a distinct operation.
As @evansd2 pointed out, a closed-path, vector shape with no fill color defined but just a stroke color defined will give you a distinct operation that defaults to a cut, but can be changed to a score, or just manually set. All vector paths defined with this same color will get imported into the GFUI as one cut/score operation to define speed, power, and focus.
A closed-path, vector shape with a fill color defined but no stroke color defined will give you a distinct operation that will default to an engrave. You can then adjust speed, power, LPI, and focus.
You want to define an object as either, not both.
If you want to make different settings for different objects, change the color value of the stroke or fill. The order of operations will depend on the color definition going from black as 0,0,0 RGB or 000000 hex to white defined as 255,255,255 or ffffffff.
Regarding “score” versus “cut”, these are just terms for the Glowforge user interface with presets. From a manual point of view, you are just defining the sames settings. It does help from a design point of view to distinguish a through cut verses a light cut that doesn’t go through and just scores the surface.