The canonical name for a mac is Apple's user manual nomenclature. In the case of airs - the MacBook Air (Late 2010) are now discontinued and sold at a discount as previous generation and today's will likely be known as MacBook Air (Mid 2011) models.
You can browse all the names at http://support.apple.com/manuals
Usually about a week after a new product launch, the latest model names will be shared publicly at this support site. These names are the ones that people will see in all the Apple knowledge base articles - so google searches for those terms will hit there and here if they are also adopted here. Try googling these terms - with and without the 13-inch parts (but with the parens) and see what the hits look like with whatever term you want to try out.
Even cooler, you can append your serial number to get all the manuals appropriate for your exact mac.
Here's the link for a MacBook Pro (15-inch, Mid 2009)
The benefit of using these names is that unlike Part numbers, SKU or other abbreviations, they don't change based on the geography and custom macs (CTO) where you upgrade the processor or ask for bundled software have other part numbers - but all macs that are of that generation are called MacBook Pro (15-inch, Mid 2009)
Often people will use System Profiler details:
Model Name: MacBook Pro
Model Identifier: MacBookPro5,3
Processor Name: Intel Core 2 Duo
Processor Speed: 2.66 GHz
I haven't seen a good list anywhere (other than Wikipedia) were the MacBookPro5,3 models are listed. I have been meaning to edit wikipedia for a while and replace all the names that don't match apple's but I have to be really bored to futz with wikitables.