Join Date: Jul 2006
Location: Vancouver, BC
Bikes: 2007 ICE Trice T; 2008 Brompton M6L; 2009 Surly LHT; 2010 Surly Cross Check
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Usually the small wheels I see are 16 or 20 inches; and yes, at least in North America this is most commonly a folding bike. However, those are usually not a diamond-type frame. If the bike you're talking about does not fold, and has a full diamond, I think it's what is called a "minivelo". Apparently those are popular in Asia.
The small wheels are in some ways more maneuverable and accelerate quickly. The bike can be overall lighter, and is not as long for the same wheelbase, so it's a little better suited to apartment living. You can also fit a big chunk of luggage on the front since the wheel is so much lower compared to the handlebars.