The terminology surrounding 'damascus' steel is rather confusing. This is what I believe to be the basic situation though:
'damascus' is a general term, and is applied to a variety of different techniques which result in these sorts of 'wavy' patterns. I believe the term is now thought to originate in the appearance of the pattern, likened to damascus fabric. Or it may be that Damascus (the city) served as a distribution centre, as the South Indian makers of 'wootz' steel took care to keep its origin somewhat secret.
I believe 'watered' is another general term, I would presume referring to the pattern again. Alternately, perhaps it is most correctly applied only to 'wootz' steel, but I doubt this. Possibly the term 'watered' might also originate in the fact that for all types of 'damascus' some sort of acidic etchant is required to bring out the pattern.
There seem to be two basic types of 'damascus steel'.
The first type (I think the oldest technique) is the type made (roughly, in layman's terms) by mixing iron with sources of carbon, and 'cooking' it in a crucible or the like. This produces a material which is hetregenous in make-up, with the carbon content varying through the steel itself. This is generally thought to have advantages in producing a relatively hard steel, which is not too brittle (as high carbon allows the blade to be hard, and also retain a better edge, but also tends to make it brittle and prone to shatter).
The first type is various called
'true damascus', 'wootz' (steel), 'ukku' (steel), crucible steel, and probably other terms as well..
The last term, 'crucible steel', is perhaps more general, not applying only to (Indian-made) 'ukku' or 'wootz', but also to similar products produced elsewhere but perhaps differing in certain respects. It seems that Central Asia and also Russia have produced 'crucible steel'. I don't believe any of this type of steel is made in India any longer, perhaps not since the 19th century? So I think all modern wootz steel is either Russian-produced, or at least produced via the Russian technique.
Wootz steel was apparently imported into classical/mediaeval Europe sometimes (esp. into Rome?), but it requires to be forged at somewhat lower temperatures than 'regular' steel of the mediaeval (& earlier) periods, so European smiths in general did not have that much success in using it.
The other type of steel seems to originate in Europe (and perhaps independently elsewhere), and is not made in a crucible or any such thing, but rather consists of pieces of steel (of varying carbon contents) being stacked together and forged, usually twisted together, producing a steel billet. This technique is various named
'mechanical damascus', 'pattern-welded/welding' and other names I'm forgetting.
The earliest types of these sorts of blades were apparently made in the late B.C. or early A.D. period by Celtic smiths, and also later by Roman smiths it appears - though many of these types were not 'twisted together' and thus would not have produced these sorts of patterns, or probably have been as durable either (this sort is often called 'piled' rather than 'pattern-welded'). The more well-known examples of this technique were made primarily in Germanic areas, including Scandinavia, and probably England (at least in Kent). Part of the reason for their introduction seems to be that the Germanic peoples in general did not have access to very high quality steel (they did not mine), and relied largely on 'iron blooms' found in bogs. The pattern-welding technique allowed for stronger blades despite the lower quality steel. Post 1100 A.D. or so pattern-welded blades do not seem to be produced very much in Europe, presumably because Germanic smiths gained access to better quality iron/steel to work with, and as pattern-welding is more time- (& skill-)intensive, these swords were generally no longer made. Though the older pattern-welded swords were highly valued even in the later period.
There are also obviously examples of Asian/Indian mechanical damascus, but I am not so familiar with their history.
In general, the 'true damascus', 'wootz' steel has more 'natural'-looking ripples, and usually the pattern is more complicated and 'smaller'/'finer'. 'Mechanical damascus' tends to produce less-random patterns, and the older examples (e.g., 7th century A.D. etc.) tend to show few, large bands, in contrast to the sort of 'rippling' of the wootz. But modern day mechincal damascus can be made in many patterns, some of them probably being difficult to distinguish from 'wootz' except by trained eyes.
just my general notion of these things. I am not an expert on this, so some details may or may not be accurate.
more links on these types of steel available on my page:
http://www.jnanam.net/shastra/
under the 'General Steel Info' section near the bottom of the page.
cheers,
--B.