Facebook Inc. Chief Executive Mark Zuckerberg has protested for years that Apple Inc. and its leader, Tim Cook, have too much influence over the social-media behemoth’s business. In 2018, his anger boiled over.Facebook was entangled in controversy over its data-collection practises. Mr. Cook piled on in a national television interview, stating that his own company would never have found itself in such a jam. Mr. Zuckerberg shot back that Mr. Cook’s comments were “extremely slick” and “not at all aligned with the truth.”In private, Mr. Zuckerberg was even more relentless. “We need to inflict pain,” he told his team, for treating the company so poorly, according to people familiar with the exchange.It wasn’t the first time-or the last-that Mr. Cook’s comments and actions would leave Mr. Zuckerberg fuming and, at instances, plotting to get back at Apple. The build-up of outrage flared up late last month in a rare public retaliation between the two tech giants that laid bare the simmering friction between their leaders, who exchanged jabs over privacy, app-tracking tools and, ultimately, their dueling visions regarding the future of the internet.