@Anonymous Coward: Watts do not have a time scale built in.
Watts are misleading. They say how fast work is accomplished / energy is delivered, but without a timeline you don't know how much work was done / energy was delivered. Power (Watts) is equivalent to speed (miles per hour): you cannot tell distance covered at a given speed unless someone tells you the time spent at that speed. You traveled at 60mph? Great, how far did you go? You can't tell unless someone tells you the time spent at 60mph.
Back to power. For example: lifting a liter (kilogram) of water on Earth could take (pardon me rounding gravity to 10m/s/s) 1/10th of a Watt, 1 Watt, 100 Watts, 1 megawatt, 1 gigawatt, or any other number of Watts. If you don't specify the time (or distance) Watts don't tell you anything because you've got 2 unresolved variables (distance and time). 1 gigawatt might've been used to lift the kilo of water to a distance of 1 meter in 1/100,000,000th of a second, or it might've been used to hoist that liter to a height of 1000 kilometers in 1/1000th of a second. (I think I got that math correct.)
If the distance was fixed at 1 meter, the difference between a 1/10th Watt hoist and a 1-gigawatt hoist is not energy, because both hoists only delivered 10 Joules of work (lifting a kilo a distance of 1 meter in 1G, rounded up). Rather, it was time of delivery: 100 seconds versus 1/100,000,000th of a second. The work accomplished was the same, but you can guess the difference in size and complexity between a 0.1-watt motor and a 1-gigawatt motor.
Similarly, a laser is a 1-megawatt laser if it delivers 0.001 Joule in a nanosecond, even if it only delivers a fraction of a joule of every second. A laser is also a 1-megawatt laser if it delivers 1 million joules per second for hours on end. There are a couple of difference between the two lasers.
One of those lasers is a few kilograms and can vaporize microscopic quantities of rock with spare wattage from a 125-Watt RTG. The other fills a jumbo jet and can puncture the skins of liquid-fueled ballistic missiles using tens of megawatts from combusting exotic chemicals. The difference between is not wattage of output (both are 1-megawatt lasers), but rather total joules delivered to target.
And you don't know the joules delivered by a power source unless time is separately specified. Watts certainly won't tell you.