The motion of the gesture is the same swiping a hand over the screen action in each instance but does do different things depending on what the phone is doing. For instance, waving a hand over the screen for the phone when the alarm is going off silences the alarm. Dismissing with a gesture is much better than having to fumble in the dark for your phone and swipe the screen to turn the alarm off.
The video also shows users dismissing an incoming call and skipping tracks in a music app using the same gesture. Previously it leaked that the Motion Gestures would work with Spotify, Amazon Music, Deezer, Google Play Music, iHeartRadio, Pandora, YouTube, and YouTube Music. You can see all of the video in the 9to5Google source link below.
Along with the demo of the gestures that leaked also comes details on the new Google Assistant that will be featured in the Pixel 4 smartphone. The new assistant has colors that move up the screen as the user talks and what the user is saying replaces the "Hi, how can I help?" prompt. An AI Assistant panel with what the user has asked slides up, the UI is also more compact.
Other cool things with the new assistant include support for back to back commands; a feature carried over from Google Home. The assistant also remembers the context of a conversation. One demo shows a person getting a text about when a flight lands, asking the assistant to show the itinerary and then having the Assistant reply to the text with the right flight information.