True for notebooks. (For years my home NAS was an old Asus EEE PC)
Desktops, on the other hand, tend to consume a lot more power (how bad it is, depends on the generation) - they're simply not designed to be a quiet device sitting on a corner continuously running a low CPU power demanding task: stuff designed for a lot more demanding tasks will have things like much bigger power sources which are less efficient at low power demand (when something is design to put out 400W, wasting 5 or 10W is no big deal, when it's designed to put out 15W, wasting 5 or 10W would make it horribly inefficient).
Meanwhile the typical NAS out there is running an ARM processor (which are known for their low power consumption) or at worse a low powered Intel processor such as the N100.
Mind you, the idea of running you own NAS software is great (one can do way more with that than with a proprietary NAS, since its far more flexible) as long as you put it in the right hardware for the job.
Stuff designed for much higher peek usage tend to have a lot more waste.
For example, a 400W power source (which is what's probably in the original PC of your example) will waste more power than a lower wattage on (unless it's a very expensive one), so in that example of yours it should be replaced by something much smaller.
Even beyond that, everything in there - another example, the motherboard - will have a lot more power leakage than something designed for a low power system (say, an ARM SBC).
Unless it's a notebook, that old PC will always consume more power than, say, an N100 Mini-PC, much less an ARM based one.