If I have a gameplay on YouTube from e.g. Black Ops 3 Anguish everything looks super fluid. When I play Black Ops 3 myself, everything seems very jerky although I have more than 60FPS. On the PC, it can't be, because it is synonymous with my laptop and the Xbox One like that. VSync is off. Normally I play with 144hz and I thought that it seems jerky to me 60hz, but that can't be because a 60FPS video looks smooth and just does not hold the game. By the way, it's the same with all games.
I hope I could explain everything understandable.
The game does not seem so fluent to you, is due to the fluctuating frametimes by fluctuating FPS. Here it is strongly recommended to use a sync technique or to cover the FPS. The problem is that this increases the input lag. But if you can live with that, that's fine.
Videos have two details that are important here for the perception.
Image compression makes small details easier to miss. There's almost always a slight blurring between the pictures, which makes a picture change more fluid than it actually is.
A video has no input from the user, eliminating any perceived delay in input. This does not weigh as heavily as the image compression, but also contributes greatly to why we perceive movies as a fluid image sequence, while we often perceive a game with the same frame rate (eg 24FPS) as reasonably playable and noticeably disturbing.
