***
At one time I saw a Watt Second meter, I think it was for calibrating industrial strobes. It might be interesting to see what the output of our lights realy is.
As already explained, a watt-second (Ws, equal to a joule, J) is a measure of the amount of electrical energy coming out of the capacitor. It isn't a measure of the amount of light energy coming out of the tube. Something that measures watt-seconds would generally be measuring electrical energy - like a standard domestic kilowatt-hour meter*.
Some manufacturers, like Paul C Buff/White Lightning, quote 'effective watt seconds' because they want us to believe that their tubes are more efficient than other manufacturers' tubes in converting electricity into light (more lumens per watt). In fact they are about the same as most - around 40 lumens per watt. The total amount of light energy emitted by a flash tube is measured in lumen-seconds.
If you are measuring flash with a hand-held meter, the best you are doing is measuring lux-seconds at a certain point. The relationship between the output in lux-seconds at that certain point and the total amount of lumen-seconds depends on how those lumen-seconds are used: ie the shape and surface of the diffuser etc as well as how far away you are from the source.
Fortunately the most important thing to us is the measurement of lux-seconds, because that's what we are using whether we call it lux-seconds or not**. That's what a flash meter tells us, in the form we need (ie f-stop at a certain film speed).
If flash manufacturers wanted to give us a piece of useful information about how much useful light energy their gear spat out, independently of which reflector was used, they could just quote lumen-seconds.
*There is such a thing as a watt-second of radiant energy, but it isn't much use to us because it includes radiant energy other than light - it has no spectral weighting. Light energy cannot be measured in watt-seconds, because a watt is not a measure of light power.
**Not 100% accurate, but good enough for the purposes of this discussion, I hope. We humans might respond to illumination in lux, but film can have a different spectral sensitivity. Light (lux, lumens etc) is measured in terms of human spectral sensitivity. Photographic light meters try to take this difference into account, at least to some degree.
Best,
Helen