Samsung also refreshed the look of the software that rides on top of Android, calling it One UI. You'll find it on Samsung phones going forward, including the foldable phone and likely the forthcoming Galaxy S10.
One UI only works with Android 9 Pie, and resembles some of Pie's design concepts. The Galaxy S9 Plus running Android Oreo is on the left; on the right you have a demo Galaxy S9 Plus with One UI on Android Pie.
The changes to multitasking are stark. Now apps are separated by panes you can flick through horizontally, rather than vertically. You can also tap an icon below to open an app or swipe up to see them all. There are a few similarities to iOS here.
If you want to ditch the on-screen navigation buttons, a submenu lets you use full-screen gestures. Hard-press where the home button should be. Swipe up on either side of the space to go back or open your recents apps.