Adobe found that click-and-collect shopping between Nov. 1 and Dec. 6 grew by 46 percent compared to the same period a year ago. A big part of the increase in digital shopping — up 18 percent during this period — is click-and-collect shopping, Adobe says.

CNBC cited a report by Kurt Salmon that says retailers have greatly streamlined this channel of buying — sometimes referred to as BOPUS (buy online, pick-up in store). Among the top performers are Home Depot, Kohl’s and Target, says the report.

"We found a few years ago, a lot of the discussions retailers were having brought all different perspectives on [buy online, pick up in store]. It was in its infancy," Frank Layo, managing director at Kurt Salmon, part of Accenture Strategy, told CNBC. "But people started to see it as a competitive advantage against Amazon building distribution centers around them."

Click-and-collect gives customers and retailers the best of all worlds, Layo observed. Shoppers can streamline their visit to the store by ordering online in advance, and get their merchandise immediately. Retailers, meanwhile, can avoid incurring shipping costs when people shop this way.