Why iOS handles downloads differently
iOS does not have a general Downloads folder the way Android does. Safari puts saved files into the Files app — usually iCloud Drive > Downloads — and videos only reach your camera roll when you explicitly send them to Photos. That extra step catches a lot of people out, so the walkthrough below covers both destinations.
The upside of Apple's approach is that nothing needs access to your library. Safari itself saves the file, so no other app sits in the middle with permission to read your photos.