Japanese Knotweed

I had a different species of Knotweed on my property but I just ran across this one on somebody else's property.

Meet Reynoutria japonica (Japanese Knotweed)-

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It has blanketed their ravine. There are thousands of them extending for a long as the eye can see.

Polygonum cuspidatum
Fallopia japonica
Pleuropterus cuspidatum
Polygonum cuspidatum var. compactum
Polygonum zuccarinii
Reynoutria japonica

Isn't this the same beast by another name? Plantfiles has these names all listed as synonyms.

http://davesgarden.com/pf/go/32028/index.html

Yes- Reynoutria japonica = Polygonum cuspidatum

There's this monster out there that is also referred to as Japanese Knotweed and also referred to as Sakhalin Knotweed although it's actually indigenous to Sakhalin Island which is north of Japan-
http://davesgarden.com/pf/go/32071/index.html
And then there is a hybrid of the two that has become a big cause for concern Special, the knotweeds are hybridizing.

I have what I was told is prostrate knotweed in the yard that I actually like as a ground cover. Are they related?

That would be Polygonum aviculare. They're both the same family and genus and they're both documented as being invasive.