Watts is a measure of power consumption, equal to something like 1 joule per second or something. Bulbs are measured in wattage as a guide to how much light they're consuming, and therefore gives an idea of how much light output they are making.
A 25 watt bulb uses less energy than a 100 watt bulb, but puts out rougly 1/4 the amount of light as well.
Wattage has nothing to do with tanks, just the bulb. We then use the wattage of the lighting to determine how much light is on the tank.
For instance, if you had a 10 gallon tank, and a 50 Watt bulb, you'd have 5 watts per gallon of water. This is a guide we use to determine what we can do with the lighting and how much lighting we need. It's just a guide, there are no set in stone rules, however, when it comes to lighting an aquarium.