On some platforms, like Instagram, people generally cannot tell if you screenshot a story. The app doesn't send a notification to the person who posted the story that you've taken a screenshot. However, there are some third - party apps or hacks that claim to be able to detect screenshots, but these are often not reliable or may violate the platform's terms of use.
In most cases, people cannot tell if you screenshot a story. Social media platforms are designed to protect user privacy to a certain extent. Taking a screenshot is a common way for users to save content they like. If platforms allowed story posters to know about screenshots easily, it could discourage users from interacting with stories. So, while there may be some rumors or unproven methods about detecting screenshots, generally it's not possible for someone to know for sure that you've screenshot their story.
Most of the time, no. For example, on Snapchat, in the past there were concerns about screenshot detection, but currently, for regular stories, there's no official way for the story creator to know if you've screenshotted. But if it's a private snap with special settings, it might be different. In general, for mainstream social media story features, screenshotting usually goes unnoticed by the poster.