No, the official model names of the computers have dates in them, e.g. "Late 2010", "Mid 2011", etc. I have, for example, an "iMac, 27-inch, Mid 2011".

My point is that they're not being consistent. They call it "the new iPad" in the presentation, but then the guy in the video calls it "the third-generation iPad".

Yeah I thought it was obvious.

Numbers are messy, it's better to have a product represented by its name and have its generation just be a property.

That's why they make the extra effort of saying "third-generation" rather than iPad3. They don't want it to be referred to as an iPad3, just as an iPad.

I was surprised they called the second one iPad2.

Apple hasn't historically had multiple names for a single product before. That's what I see as sloppy about it.

No, they didn't. The iPhone 4's model name is "iPhone 4", same for the "iPhone 4S". This one's model name is, according to the presentation, "the new iPad". You never see Apple refer to "iPhone 4" or "iPhone 4S" as "the n-th generation iPhone".

I'm not arguing the evolutionary/revolutionary angle, just that it's completely unprecedented for Apple to use TWO DIFFERENT NAMES to refer to ONE PRODUCT in their marketing materials.