Older computers used to use a latching switch (similar to the typical light switch) for power and a momentary switch for the reset button. The latching switch was part of the power loop and broke the power connection (at least, this is close enough to the truth to not matter here).
New computers use momentary switches for both power and reset (which is why your friend could swap the switches and have them function the same). Momentary switches close a "signal loop" (not a technical term) that suggests to the motherboard that you want to shut it off. The motherboard detects the signal and then handles that by communicating with the OS. Pressing and holding for 4 seconds will force a shutdown without sending a terminate signal to the OS.
If you are experiencing the long-press behavior, your button may be sticking. You can try cleaning the switch to ensure there is no gunk preventing the button from springing back after you press it. If you need to replace it, google "ATX Power Switch Case 2-Wire"
Note that any momentary switch will work and if you have a soldering iron, you can get one from Radio Shack (etc.) and attach the old power switch leads with jumper to the new switch.
I have an old case with the older style power switch, but I have been using the reset button as the power-on button for newer motherboards for many years.
In fact for these newer two lead ATX, ANY switch will work: light switch, doorbell etc. You could hook up a light switch to the leads from the jumper and then flip it on/off rapidly or on/wait 4 seconds/off to force shutdown.
WARNING: OLDER SYSTEMS WITH MORE WIRES/BIGGER LATCHING SWITCHES CARRY DANGEROUS_AND_WILL_KILL_YOU VOLTAGE