Screenshots and screen recordings in the app
When you take a screenshot or a screen recording of a snap, a story or a chat in the Snapchat app, the other person is notified. On stories, a screenshot icon appears next to your name in their viewer list.
This works the same on iPhone and Android.
Saving a public story from the web
A web viewer doesn't use the Snapchat app or your account. When you download a snap from a public profile here, nothing happens inside Snapchat, so there's no screenshot notice.
You also get the original file (MP4 video or JPG photo) instead of a lower quality screenshot.
Be fair to creators
Public doesn't mean free to reuse. Keep downloads for personal use, and ask the creator before you repost anything. Private snaps and chats should stay private.