You are asking the wrong question. The right question is:
How a website knows if a video has been watched or downloaded?
And the simple answer is: It cannot know for sure.
The example I'll use for this argument is the way how most Linux users watch videos. The backend of video display on Linux is today
ffmpeg (which is used by
vlc as well). The backend supports youtube URLs by means of
youtube-dl (and youtube-dl is/can be used in VLC).
When a user types (or I do it, since I just typed this to make a test):
The video is downloaded to my machine before playing.
But wait, when I watch a video through a browser is isn't being downloaded right? Wrong. When you watch a video through a browser the video is downloaded to your machine alright before being displayed. The video need to reach your machine's memory at some point to be played.
Therefore there is (almost) no difference between using a streaming player (
mpv) and watching from a browser. There are just a couple of differences. When you watch through a browser you also see the rest of the website, the banners are fetched, the JS is executed. If someone on the streaming website can look at the webserver logs he can conlude whether you saw the page through a browser or not (stream players do not have JS engines).
A website maintainer can tell if you looked at a webpage or not when you were watching the video. He can, therefore, tell is you used the browser interface to his website or a streaming player. But he cannot tell the difference between a streming player and a download, because the steaming player already performs the download anyway.
Can a website claim that stream players are the same as downloads of a video? Not really, the number of people using stream players is big, notably VLC.
One of the biggest reasons that people started using streaming players was to escape from using the Flash Plugin (which is famous for being particularly buggy in terms of security). This is less of a problem today (with HTML5 streaming implemented widely), but still a reason why so many streaming players are used.
Disclaimer: When DRM comes into play things change. Unfortunately (fortunately?) I have almost no experience with DRM