Wal-Mart (NYSE:WMT) has made major strides when it comes to becoming a serious digital player. By offering free shipping on eligible orders over $35 and allowing in-store pickup and return for online orders, it's even fair to say that the brick-and-mortar chain has established itself as a real rival for Amazon (NASDAQ:AMZN).

Cyber Monday, however, showed that while Wal-Mart may have upped its game, Amazon is playing on a different field entirely. The online retailer not only crushed its nearest rival, it actually conducted more transactions than the next 49 top retailers combined, according to one report.

A Wal-Mart pickup tower.

Some Wal-Mart locations offer in-store pickup towers for online orders. Image source: Wal-Mart.

How dominant is Amazon?

Cyber Monday -- the Monday after Thanksgiving, when, so the story goes, people are busy avoiding work after the long holiday weekend and instead shopping online -- was the biggest digital shopping day of the holiday season so far, with the top 50 retailers processing 14.5 million online transactions, according to data from Hitwise. That beat out Black Friday at 13 million and Thanksgiving Day at 12.5 million.

Amazon accounted for nearly 60% of the total number of transactions on Cyber Monday, with 8.6 million, according to Hitwise, while Wal-Mart came in second with just over 1.2 million, good for 8.5% of the total.

Amazon was nearly as dominant on Black Friday when it processed 7.1 million transactions, or 54.9% of the total.  Wal-Mart's best day online was actually not Black Friday or Cyber Monday. The retailer processed 1.7 million transactions on Thanksgiving, still well below Amazon's 5.6 million, according to Hitwise.

In addition, Amazon handily beat Wal-Mart when it came to online visits, scoring 102.5 million on Cyber Monday compared to Wal-Mart's 32.2 million. Interestingly enough, when it came to converting visits into sales, Amazon came in fourth behind L.L. Bean, Shutterfly, and Old Navy. Of those three, only Old Navy made the top 10 in transactions, coming in sixth with 216,771 or 1.5% of the total on Cyber Monday.

Is Wal-Mart a real rival?

Saying Wal-Mart is No. 2 to Amazon when it comes to digital retail is a bit like saying the Canadian Football League is second only to the National Football League. That's, of course, true, but the gulf between the two football leagues can't be closed in any meaningful way while Wal-Mart has a chance to keep growing.

Hitwise didn't provide dollar figures, but we can do some math. If we start with Adobe Analytics data that $6.59 billion was spent on Cyber Monday, and if we assume that each retailer's sales total correlated to its transaction share, then Amazon's 59.6% of Cyber Monday transactions would equal $3.92 billion in sales while Wal-Mart's 8.5% transaction share would come out to $560 million in sales.

Wal-Mart certainly isn't Amazon, but it has been steadily growing its digital business while leveraging its physical stores to offer a true, omnichannel shopping experience. The retailer is still in the early phases and it's already well ahead of Target (which came in third in Cyber Monday transactions with 4.6%) and Best Buy (which was third in visitors with 18.5 million).

It's reasonable to expect that Wal-Mart will gain on Amazon, but it's not certain that the brick-and-mortar chain's growth will come at the online leader's expense. But it's possible that both companies will continue to use size, buying power, and higher technology budgets to keep putting the squeeze on smaller retailers.

Cyber Monday showed that Amazon remains firmly in control of the digital world. Wal-Mart, however, at least put a flag in the ground and showed it's no longer ceding the digital part of the retail business to its rival without a fight. 

John Mackey, CEO of Whole Foods Market, an Amazon subsidiary, is a member of The Motley Fool's board of directors. Daniel B. Kline has no position in any of the stocks mentioned. The Motley Fool owns shares of and recommends Amazon. The Motley Fool recommends Adobe Systems. The Motley Fool has a disclosure policy.