Its slightly different for measurement of self-luminous sources (e.g. a display) vs. reflective samples (e.g. a print). For the display, the SPD is whatever light comes out of the screen*, there is no separate illuminant involved. For the reflective print, the SPD is the product of the reflectance spectrum of the print and the illuminant (D65, D50 etc.).
*ignoring any ambient light reflected from the surface of the display, which you usually try to minimise.