The screen is called Launchpad and is a feature built-into macOS. First introduced in Mac OS X Lion 10.7, it displays a grid of icons corresponding to installed apps. This feature was originally inspired from iOS which displays a similar grid of icons for installed apps.
This gesture is pre-defined for Trackpad, and can be turned on/off under System ...
I use this page to determine what each swipe does. What you're describing is called "Launchpad".
Use Multi-Touch gestures on your Mac
It looks like this when you open it:
screenshot of Launchpad
This is the swipe you're describing
Double tap on that word.
Select a word: double-tap on it.
Select a sentence: tap on the text with three fingers.
Select a paragraph: tap on the text with four fingers.
Bubble menu: bring up the shortcuts menu by tapping once with three fingers.
I figured out how to do it with BetterTouchTool. In BetterTouchTool the action is called "move right/left a space.
I set up an action for both 2 finger swipe left, and 2 finger swipe right on the trackpad and left the magic mouse with the standard 2 finger swipe.