The desktop app reads what your machine is already playing and writes down what you actually listened to.
Windows keeps a media session for whatever is playing, the same one your keyboard's play button talks to. The desktop app reads it and writes down what you heard, whether that is Spotify, a browser tab or any other player. A track counts once it has played for a minute.
It reads titles, not audio. Nothing is recorded, nothing is uploaded except the name of what played, and nothing is written while the machine is sitting untouched.
A log is a score you chose to give. A play is something that happened. The app keeps them apart, because the gap between them is the interesting part. A record you played forty times and never rated says something, and so does a five you played once.
It also saves you the typing. What you played shows in the strip along the bottom of the window, and rating it is one click from there.
It starts when the desktop app opens and says so in the window the whole time. Turn it off in Settings and it stays off on that machine until you turn it back on.
Your play history is yours and nobody else can read it. A record's own page shows how many times it has been played here in total, across everybody, without naming anyone.