I don't believe that's quite correct.
A display tank surface area is typically much larger than a refugium surface area, so multiple lights are needed to illuminate the display whereas one light will typically be sufficient for a refugium.
A display tank is typically deeper than a refugium & needs strong light intensity to reach the bottom. The algae in a fuge is at the surface, again needing less intensity in comparison & so less wattage needed.
Also, a typical light used for a display has a wider/ fuller spectrum range, but algae in a display only utilise the spectrum in the PUR range. So a refugium light just needs to provided PUR spectrum, meaning less watts needed in comparison.
In my case, an algae scrubber completely out competed the nuisance algae in the display. I don't believe its only a matter of the scrubber algae out-competing the display algae/cyano for nitrogen - phosphate - & various specific trace minerals advantageous for algae photosynthesis. I believe there's also a strong bacteria specific link to algae & its existence. Once a specific nuisance algae's symbiotic bacteria population is overcome by the filtration algae's symbiotic bacteria strain the filtering algae's job is much easier, & the photo-period required is mostly dictated by the volume of nutrients that need processing.