Consumer behaviors can be hard to change. That explains why the majority of consumers still head to their nearby drugstore to fill or refill a prescription.

But drugstores are increasingly digital—and they’re not just for prescriptions. And if Amazon.com Inc., Walgreens Co., CVS Health and some well-funded digital pharmacies have their way, digital drugstores will soon transform from mainly offering prescription order and pickup or delivery services into online healthcare shopping malls.

Because drugstores—and the pharmacists who work there—often have close relationships with their customers, many consumers give their druggists a lot of steady business. For example, 55% and 40%, respectively, of web shoppers on Walgreens.com and CVS.com are repeat buyers, says e-commerce measurement firm Connexity. That significantly outpaces the 33%…

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