In most cases there is little to no difference. However in certain rarer situations you do need to wait longer to make sure the capacitors are fully empty. Like if you need to open up the computer it is best to leave it unplugged for a few minutes to make sure the capacitors are drained because it is better safe than sorry.
Another situation is something my IT mentor called “letting the demons out”, sometimes with less than common hardware (beta builds, custom boards, or just old stuff) or in weird failure cases your system didn’t shutdown properly and the firmware bugs out, so you let it sit unplugged for 5-10 minutes and then start it up and it works, sometimes you even remove the CMOS clock battery to make sure everything is nice and clear (this can require you to fix the computer’s clock if it doesn’t use network time).
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