Source: Facebookbrand.com.

According to a recent report, Facebook (NASDAQ:FB) is killing Alphabet's (NASDAQ:GOOG) (NASDAQ:GOOGL) Google on the digital display-ad front. The social network's display revenue was up some 40% compared with the prior year, according to the report from IgnitionOne. The search giant's, meanwhile, slipped 19%.

That's a stark contrast, to say the least. IgnitionOne's release began: "Facebook Clobbers Google in Display Growth," and outlets covering the release continued the doomsday narrative.

But there's much more to the story. And Alphabet investors should find it more to their liking.

A number of trends are intertwining today
While IgnitionOne chose to highlight the digital-display ad war in its title, the report covers much broader ground. It examines year-over-year changes in digital ad spending for the third quarter, and many of those look good for Google, which we now also can see reflected in the search giant's quarterly numbers.

Paid search, a mature area of digital advertising and Google's bread and butter, was up 12% over last year. What's more, Ignition One's research found that both the click-through rate and the cost per click on ads were on the rise, "pointing to more expensive but efficient ads."

IgnitionOne chalked that situation up to "sophistication in mobile advertising" that may be driving overall spending increases.

Also a positive for Google, mobile search remains a particularly large area of ad spending growth, even if that growth is slowing. The report pegged year-over-year mobile search spending increases at 56%. That's down from last year's 64%, but still impressive.

OK, which one is Muhammad Ali?
Grabbing the spotlight in the report, however, was Facebook's fast rise and the online ad war that's getting hotter with each passing quarter.

"While Google still owns the majority of display spend, Facebook is quickly catching up," said Will Margiloff, CEO of IgnitionOne. "And with Facebook's debut of Atlas and Google's response of Custom Match, it's clear that these two heavyweight champs intend to keep going at each other in the ring like Ali and Frazier. It's only a matter of time before we find ourselves with another Thrilla in Manila on our hands – neither of these players is going down without a fight."

At first blush, the display-ad numbers look like an early knockdown, or at least a two-point round for Facebook. But that's not quite the case here.

Putting numbers into context
What the report doesn't mention is that display is a considerably smaller part of Google's ad business than search. In 2014, Google brought in more than $38.4 billion in search ads, according to eMarketer. That's nearly two-thirds of all its ad revenue globally.

Ads taken through Google's AdSense display network, meanwhile, made up about $14.5 billion, or 22%, of its overall revenue.

Revenue from its own websites -- largely fueled by search -- was also growing at a much faster pace (roughly 20%) over the past two years, compared with the display networks growth of 7% in 2014 and 6% the year prior.

We also need to keep in mind that the IgnitionOne report examined just one quarter, and looked at a smaller window of time -- three months rather than the trailing 12, for example -- lends itself to a potential skewing of results.

There's no question that Facebook is the faster-growing company of the two. Its year-over-year revenue came in 41% higher in the third quarter, nearly double Alphabet's 21%. But Alphabet is also a more mature company, having conquered search long ago and built up a leading position in video. Perhaps its most pressing challenge is to keep its numbers growing as it transitions from desktop search to the so-far-less-lucrative mobile search market.

Facebook, on the other hand, is still in its rocket-ship phase. It's now reaping the harvest of the mobile seeds planted years ago, and it's still figuring out how to monetize some of its most popular mobile products, such as Instagram, Messenger, and WhatsApp.

The bigger picture provides a better view
With a trailing-twelve-month PE of over 100, Facebook is also selling at a significant premium to Alphabet, so expectations will remain much higher, and any slip-ups will be punished much more severely.

A headline can be quite misleading. The IgnitionOne report carried good news for Facebook, but it had plenty for Google investors to like as well. The display number is one worth watching. But it's only one piece of Google's ample digital-ad business, and investors shouldn't make assumptions about the health of the overall business based on one number from a third-party report.

Google's latest quarter gave shareholders reason to remain confident in its direction, and the IgnitionOne report provides little reason to second-guess.

John-Erik Koslosky owns shares of Alphabet (A shares) and Facebook. The Motley Fool owns shares of and recommends Alphabet (A shares), Alphabet (C shares), and Facebook. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.