Nope. Apple's official name is "Apple Extended Keyboard II". That's what's written on it. The other one is officially "Apple Keyboard II", which is what is written on that one.
The confusing one is the Apple Standard Keyboard, whose official name is simply "Apple Keyboard". "Standard" is conventionally added to the name to differentiate it from other "Apple Keyboard" products, as opposed to the alternative product, the Apple Extended Keyboard.
There are at least two versions of the Apple Keyboard II. The common one is a bog standard Mitsumi hybrid switch (buckling rubber sleeve) over a single membrane sheet. There is also an Alps-mount version, which has an SMK latching caps lock switch — it's not clear whether SMK made the whole keyboard, or whether the OEM just fitted an SMK switch to a product with completely different switches. There's only one photo of it that I can find, and Ripster stole that from someone else. I've never managed to find diddly about that version, and all the ones I've had were likely Mitsumi (they all felt equally terrible, and the one I have left is Mitsumi).