A snapshot of the global smartphone market issued Thursday by Canalys shows just how big a dent Apple’s iPhone made in the cellphone universe last quarter.

With a surge of nearly 6.9 million shipments in calendar Q3, the iPhone leapfrogged past RIM RIMM and Motorola MOT to grab 17.3% of the smartphone market.

That put Apple AAPL in second place after Nokia, and helped cut the market-leader’s share from 51.4% to 38.9%.

It also helped expand the entire smartphone category, which grew 28% from the same quarter last year to reach 40 million phones. The much larger cellphone market, by contrast, grew 3%.

Canalys also reports that Apple grabbed the No. 2 spot in smartphone operating systems, as the next table shows. Nokia’s Symbian still dominates with 46.6% market share, but that’s down sharply from 68.1% last year. RIM, Microsoft MSFT and Linux also registered gains, but nothing that compares with Apple’s.

The Canalys report came the same day as a survey of business users that showed the iPhone leading all other smartphones in terms of customer satisfaction. See J.D. Power: iPhone beats BlackBerry.

However the iPhone’s reign as No. 2 could be short-lived, according to Canalys. The U.K.-based research firm expects RIM to overtake Apple in the December quarter. RIM is selling three new products this holiday season — the Bold, Storm and Pearl 8220. If Steve Jobs has any more iPhones up his sleeve, we won’t see them before Macworld in January.