Square bet the future of “buy now, pay later” on Afterpay, acquiring it for $29 billion. Investors should spread their chips around.

The deal unleashed a flurry of buying not just in online checkout carts but in the stock market. Shares of other so-called BNPL players, including Affirm Holdings and Zip Co., jumped after the deal despite the fact that their giant competitor teamed up with Square. The thinking appeared to be that Square’s willingness to pay a premium for one of their peers shows that fears about installment payments becoming commoditized are overblown, and that the market is overall poised for huge growth.

Even if it seems counterintuitive, there are definitely reasons to hop on the bandwagon. BNPL providers don’t all do exactly the same thing: Affirm, for example, also offers larger, longer-term point-of-sale loans for bigger purchases. Overall, BNPL likely represents less than 3% of e-commerce globally, and about half of BNPL users recently surveyed had used more than one service, according to payments research firm the Strawhecker Group. So there is likely room for volumes to continue to grow sharply. Plus, based on the multiple of forward sales for which Afterpay was acquired, even at a relative discount Affirm could still plausibly trade well over $70 per share, according to Autonomous Research analyst Rob Wildhack—several dollars above where it is now.

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There might also be some attractive trades elsewhere. For one, PayPal Holdings has slipped this month. Yet PayPal also offers installments via its payment button and in some ways competes with Square to provide payment services to merchants. But PayPal’s installments work within its wallet already, so it doesn’t even necessarily require additional merchant buy-in to drive volumes still higher. If consumer awareness of BNPL grows broadly, PayPal would very likely be a beneficiary.

Another sometimes-competitor to Square for merchants, Shopify, is also down in August. Here too, Shopify would also likely be lifted by a rising tide of BNPL as it offers installments via its Shop Pay service. Notably, Affirm is its partner for the types of smaller, shorter-term installments that compete with what Afterpay does.

There was also a post-Afterpay deal dip for shares of firms that enable merchants to accept payments and banks to issue cards. Those included Fidelity National Information Services, Fiserv and Global Payments. The thinking may be that BNPL is going to supplant traditional payments and cards.

But things aren’t so cut-and-dried. These firms often partner with installment providers to help very big merchants to start using them as a payment type, and for lenders to tap into the checkout cart. Card-issuing banks, as well as networks Visa and Mastercard, offer a variety of ways to split payments and facilitate alternative lending types in online checkout carts. Such services may not have consumer brand-name buzz, but they can appeal to merchants as white-label solutions that wouldn’t risk losing any customer loyalty to the BNPL providers themselves—or the super app digital wallets that now offer them.

Cards are also part of the BNPL process today. Providers use virtual card credentials, like those offered by Marqeta, to help customers make purchases in-store or at merchants that don’t specifically offer installments. Many people pay off installments with debit cards, and in some cases they can even use a credit card.

Plus, big payments incumbents are poised to be boosted if there is a sharper swing of the pendulum back to in-person shopping, as cards remain a dominant noncash way to pay in stores. BNPL providers are moving in-store, and may be major players there in the future. But e-commerce is for now their main stamping ground.

Investors aren’t wrong to bet now on paying later, but they may need to think bigger.

Write to Telis Demos at telis.demos@wsj.com