Just to add and reiterate from some of the above;

the wattage is the power consumed as in you pay for (in KWHrs, one unit is 1 KW for 1 hour, 2KW for 30 mins etc.)

the bulbs when they say equivalent, means light intensity equivalent, (measured in Lumens but you will not see a Lumens rating on most bulbs.)

So, if you had 3 x 40W = 120W before, and you now have 3 x 20W = 60W, your electricity bill will be half as much EXCEPT energy saving bulbs strike up similar to a fluorescent strip, and use more power during start up than during use, so this is only true if you don't keep turning them on and off.

Regarding the safety you mention, the new bulbs are far more efficient so more of that power is used for producing light, hence less loss through heat, hence running cooler and safer.

Cable warmth is related to the power. the more current (measured in Amps) the warmer the cables. Current (I) = Power (P)/voltage (V) So, the voltage remaining the same, the lower the power (in Watts) the lower the current (in Amps) and the cooler the cables.