eBay and PayPal remained tight even after the two headed to splitsville in 2015. That's bound to change in the near future now that the auction site has decided to offer an integrated payment system built by Amsterdam-based company Adyen. The move will give way to a more seamless payment experience -- no need to log into another website to pay -- since Adyen's product (already used by Netflix and Uber) is purely a back-end payment service.
You might encounter the new payment system as soon as the second half of 2018, when the e-commerce giant deploys it (on a small scale) in North America. Its availability will expand in 2019 and the year after, until all sellers have been transitioned to the new system by 2021. eBay has an existing contract to continue offering PayPal as a payment option until July 2023, but neither company has announced if they have plans to extend that partnership beyond that point.