What exactly do you mean by "not the same thing"? Using a device means moving your eyes, among other things. I don't exactly stare at a specific point on the screen for the 63 Hz visual persistence to take effect and I'm pretty sure 95% of the other individuals of this world don't do that either
It's not magic. :) You DO see it. 500 Hz for the median observer; above 800 Hz for some individuals. https://doi.org/10.1038/srep07861
There is still some ability to percieve strobing at a steady state though, even if the amplitude is reduced by visual persistence.