An attemporator controls steam temperature while a desuperheater removes whatever superheat there is in steam and reduces the temperature to a point at or nearly at saturation temperature.
Attemporators are generally found in and/or associated with boiler steam, in zones where too high of a temperature affects something down stream of that point. An attemporator might be used between superheater zones in a multi-zone superheater boiler or in a re-heater zone to control reheater outlet temperture.
Desuperheaters are generally found in steam lines away from the boiler or boiler outlet piping where there is a downstream use for saturated steam.
Desuperheated steam is generally controlled to 5F - 10F above saturation (depending on the sophistication of the device) because if the temperature is controlled at saturation when it goes below the saturation line into the moisture region, the temperature controller cannot detect this.
I'll agree that desuperheaters are usually used to reduce superheated steam temperatures to just above saturation but you could just as easily change the temperature set-point to anything you want couldn't you?
To me it is more of a connotative thing rather than a denotative thing.
I think the 'key' is Fisher's in statement in the header "...to control or reduce steam temperature."
Attemporators just knock the temperature down a little bit, and I don't remember them being real fine control, while desuperheaters have to control to a very fine point to avoid going below the sat line and have to control to this point often with the amount of SH upstream of the DSH varying. Or at least the ones I put in had to.
My company makes desuperheaters, and there is a difference only in the way you wish it to be. It is basically saying, all desuperheaters are attemperators, but not all attemperators are desuperheaters. It is just how the individual wishes to classify the product.