SAN FRANCISCO – Five years after popularizing the term “app” and sparking a mobile-software boom, Apple is losing its advantage in smartphone applications to Google, diminishing one of the iPhone’s selling points.

Sales of applications from Google’s online store doubled in the fourth quarter from the prior three months while Apple’s revenue climbed 20 percent, according to market researcher App Annie.

And some software firms such as Ngmoco, which historically wrote programs for Apple before Google, have put the two operating systems on equal footing – in some cases developing for Google first.

Apple was for a time the biggest smartphone maker and its mobile operating system was the most widely used, in part because of the company’s leadership in downloadable games, magazines and productivity tools. It fell behind in software to Google’s Android in 2010 and ceded the top hardware spot to Samsung Electronics last year.

After trailing Apple for years by number of apps available, Google caught up last year, saying in October that its Google Play featured 700,000 applications, the same number Apple boasted that month.

“It’s growing exponentially – we’ve seen an inflection point the past six months,” said Clive Downie, chief executive officer of the Ngmoco unit at DeNA, which bought the apps maker in 2010. “We treat Android and Apple the same. They are equal partners to us and we put equal amounts of resources toward both platforms.”

Google’s gains are mirrored by the companies’ share prices. Google closed at a record high on Feb. 1, while Apple’s stock has tumbled 37 percent from its peak in September.

Three of four handsets sold in the $260 billion global smartphone market are powered by Google’s Android operating system. To press the advantage, Google has been making it easier for programmers to build apps and simpler for users to find and purchase them.