Syncing, as Apple uses that term, is a transfer of the media file from the computer library to the disk in another one of your other devices. This is supported for mobile devices. It does not rely on iCloud. Sync movies between your Mac and iPhone, iPad, or iPod touch - Apple Support
Home Sharing allows users to access media files that are on a computer from your other devices (computer, mobile, Apple TV box). It uses the home network, not iCloud. Use Home Sharing to share media from a computer to other devices - Apple Support. Home Sharing is not supported on third party devices with the Apple TV app (e.g. smart TVs). For the Apple TV box, Home Sharing uses the Computers app instead of the TV app.
iCloud Photos allows home videos in your personal iCloud storage, for access anywhere on any of your devices through the Photos app. It should not be used for “recordings” that are commercially copyrighted, per its terms of use. Expect Apple to monitor that. Also, videos are quite large in size (compared to music), so you may need to upgrade your iCloud plan if you use it for many videos or long videos.
Apple Music (and iTunes Match) are special, as that allows uploading your own audio media files to Apple servers, for playback on any of your devices anywhere. This uses iCloud (but not your iCloud plan).