It depends on two things
The first is your macOS version. The second is whether the wallpaper is a video or a Wallpaper Engine scene. Those two variables produce three different behaviours, which is why the same setup can look right on one Mac and static on another.
Video on macOS 26 and later
A video wallpaper plays behind the lock screen. The clip you set on the desktop is the clip you see when you wake the machine, so a short ambient loop reads as a moving lock screen rather than a photograph.
This is the case most people want, and it is the newest one. If you are on macOS 15 and see a still image where you expected motion, the version is the reason, not the file.
Video on macOS 15
The lock screen holds a still frame of the current video. The desktop still animates normally. macOS 15 does not expose the lock screen surface in a way that lets a video play there, so the app takes a representative frame instead.
Scenes stay on the desktop
Wallpaper Engine scene wallpapers are set on the desktop on every supported version. A scene is a live render rather than a file the system can hold up on its own, and the lock screen is not a surface the app draws into.
Rotation
Playlists rotate between wallpapers on both the desktop and the lock screen, so a set of clips can cycle rather than one staying fixed. Menu bar controls let you pause the current wallpaper without opening settings.