The headlines are alarming to say the least. Prime — the Amazon.com, Inc. (NASDAQ:AMZN) service that offers free shipping and access to a large library of streaming video content — is more popular than memberships in brick-and-mortar shopping club Costco Wholesale Corporation (NASDAQ:COST). It’s something heavy-duty for current and prospective owners of COST stock to think about, as the chain of discount warehouses had appeared mostly immune to the retail apocalypse Amazon has spurred.

But what if it wasn’t true? What if there was more to the matter than just what the headlines suggested?

As it turns out, there is.

More Prime Customers Than Costco Members

In the grand scheme of things, it’s all part of a massive contest. What’s a retailer willing to do to attract customers? And what will it ask customers to give for the right to be a patron?

For Costco, an annual fee of between $60 and $120 grants access to significantly-discounted groceries and basic necessities sold in stores. It also offers online shopping, though that’s not a big piece of its revenue mix. Amazon charges $100 per year for free two-day shipping on most of its goods sold online, but a Prime membership also includes access to a large assortment of digital content. Walmart Inc (NYSE:WMT), meanwhile, doesn’t require anything to shop online or offline, but for consumers willing to spend $35 per purchase and wait two days to get it, they’ll avoid shipping charges.

To the extent it is a contest, to the chagrin of COST stock holders, Amazon looks to be winning it. Amazon CEO Jeff Bezos recently disclosed there are more than 100 million paying Prime members, versus only about 90 million Costco club members. Moreover, analysts say more than 90% of Amazon’s Prime members reliably renew their memberships, versus Costco’s renewal rate of a little less than 90%.

This doesn’t have to spell out the beginning of the end for Costco Wholesale though. In fact, it doesn’t even come close to doing so.

Not Apples to Apples for COST

In a purely numerical sense, it’s a concern. There’s far more to the matter than just numbers though.

Chief among the rebuttals to the suggestion is that many consumers aren’t choosing Costco or Amazon. They’re choosing Costco AND Amazon.

MoffettNathanson recently ran the numbers, determining that 57% of Costco’s members also pay for an Amazon Prime membership, up from 13% just a few years ago when Prime was in its infancy. And, though Amazon with or without Prime has clearly proven problematic for many retailers, the MoffettNathanson report accurately points out that “Over those five years, as membership overlap exploded, Costco has shown steady revenue and membership growth.”

A willingness to participate in two different discount programs, MoffettNathanson concludes, points to two very different value propositions. Costco is perfectly-positioned to sell groceries that must stay cold (and can’t be jostled) while at the same time offering bulky goods that don’t lend themselves to shipping. Amazon has mastered the art of cost-effectively packaging multiple small items into one large box, and keeping consumers engaged with a great deal of “value add.”

That’s the assessment from a recent survey performed by UBS anyway, which determined “The results of our survey provide a compelling reason to believe there is plenty of room for both Costco & Amazon to thrive in the current environment.”

Bottom Line for COST

Don’t read too much into the message. Costco is holding its own by being something slightly different than Amazon. But Bezos has proven in the past he likes to be disruptive just for the sake of being disruptive. Never say never.

Now a couple of decades into the Amazon era though, and nearly four decades into the club/warehouse era, both sides of the table have pretty well learned how to defend their turf. They’ve turned their craft into an art and a science. And they’ve figured out what keeps their respective customers coming back.

Sure, Costco would love to have all the business Amazon is doing. But it’s not like Costco is losing business to Amazon. Owners of COST stock can take comfort in knowing, as the MoffettNathanson report put it, “Americans appear to be buying into the concept of owning two ‘shopping’ memberships as the value proposition is fundamentally different.”

As of this writing, James Brumley did not hold a position in any of the aforementioned securities. You can follow him on Twitter, at @jbrumley.