I see some datasheets of power resistors where power ratings are in Watts [W] and some in [WS] which I don't know what they mean.
What is the difference between them?
Example of datasheet
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TL;DR; It's my thinking that the S is simply relating to the package being smaller.
Resistors from different manufacturers for a given power rating tend to be similar in size - the power rating effectively becomes a de facto way of identifying package size and vice versa.
As such it's plausible that they are using the prefix S to indicate that it is the higher rated resistor, but with the physical size of the next power rating down. If you go through all of the tables in your question, you'll find this holds true.
To back this up, if for example you take the SR Passives example, the part number for say a 1k 0.25W resistor differs between "CF1/4WS-1K" for the smaller package 3.2mm long package, and "CF1/4W-1K" for the larger 6mm long package. Both resistors are rated for 1/4W.
If you look at the Tecla & Chiara example, they seem to separate the two in a similar way - the ones without the S suffix are under the label "MF", and those with the suffix are under the label "MFS", which are likely the series names.
If it were representing an energy - Watt-seconds as suggested - then it would be Ws, not WS per SI unit capitalisation. I could understand if one failed to make this distinction, but the fact that three fail makes me highly sceptical. As a specification it also doesn't make much sense without context.
For example, could I run a 1Ω "2WS" resistor with 500V across it for 2ms? That would not exceed 2 Watt-second, nor exceed the voltage rating, however it would result in a 500A surge through the resistor. Is this allowed? Would the "2W" version be able to withstand this? Could it withstand more? It would be a meaningless specification.
They are both Watts. The "WS" has been used by some Chinese manufacturers for the power rating of miniature resistors. It probably started as a mistake made when copying some other manufacturer's datasheet, and the mistake has been copied to new datasheets and to the datasheets of other Chinese manufacturers that shared the same facilities, staff and technical data. Many of the higher-wattage rating miniature and high surge resistor lines end in "S" (e.g. MF/MFS, W/WS). I have seen this type of error propagated in other specifications and datasheets copied among the different names of the Chinese manufacturer.
Bourns has a WS series resistor, which is a wire-wound, high-surge resistor. The datasheet has a standard and miniature version, and both use "W" for power.
MFR's metal film resistors datasheet states that the MFS (miniature) resistors have twice the continuous power rating as the standard (MF) resistors, as does KOA's. They use "W" for power rating in their miniature lines.
One rating (W) is average power over some poorly defined integration time, the other (Ws) is energy in a pulse application.
Note that voltage limits are also given and apply even in the pulse service. Basically as long as you stay within the average power, the thing will not overheat and if you have chosen a pulse rated part the energy limit is specified in the Ws figure.
You typically see pulse rated parts used for things like inrush limiting.