A led light uses a "driver" meaning a circuit that drops the ac down from line voltage to something closer like 12 volts and then rectify's it to dc. There are probably many different ways this is done.
There it also likely another circuit that "PULSES" the DC voltage at around 1khz at a 50% duty cycle resulting in a 50% power savings again because it is only on half the time, flashing so fast the human eye cannot see it.
The circuit board likely has a heat sink built onto it to protect the power transistor that will melt without it.
Short answer, yes the led use much less power and produces little heat, but the circuit board can produce quite a high temp in a small spot. I haven't heard or witnessed a glow on leds, they can be dimmed by dropping the current across them.
If you turn off the switch, your cutting off the power to the circuit feeding the light and there is likely a capacitor that works like a "shock absorber" to limit the current surge in the circuit. This also slowly bleeds off the power causing your electronic wall chargers lights to slowly dim out after you unplug them. Haven't seen a glow, but I cannot think of any other reason for it.
CFLs use a "ballast" meaning a transformer that raises the line voltage to 600v or more to ionize the gas in the tube causing it to glow. The transformers can get pretty hot. The tubes still glow for a long time after they lose power as the gas de- ionizes.
I just Googled the glow on electronics websights, it is fairly common it seems. The general consensus is that there isn't enough current available in a Romex capacitive situation to cause a glow. The most likely culprit they think might be a switched neutral leaking just enough current to make it glow... soo.... good time for some electrical safety.... don't assume that because the switch is off, that the neutral is dead as well... on three phase lighting, that will kill you!
