A screenshot can have metadata, but it usually does not carry the camera exposure details of the image shown on screen. The fields depend on the device, operating system, application, and later export steps.
The screenshot file may record its dimensions, color profile, creation time, or software. The capture time refers to when that screenshot was saved, not necessarily when the displayed photograph was taken. A screenshot may retain other metadata added by an editor or file manager.
If a screenshot is shared through a service or edited before you receive it, the downloaded copy may have different fields again. Check the file itself with an EXIF viewer instead of assuming every screenshot follows one format.
Little or no EXIF data is normal for screenshots. It does not show that the image on screen was AI-generated. If you are checking the underlying photograph, try to find and inspect its original file. See how to view EXIF data for more ways to check a file.