CONFUSED ABOUT WHERE THE SONG LIST IS STORED?

Had an issue earlier today with one of my players (a Node 2 could not see or open the library). Turned out to be a connection issue with my Wi-Fi Extender but in the process of trying to sort out where the problem was I noticed that that when I looked at the diagnostics I saw that the total songs for that player was zero songs, never seen that before or had this problem before...anyway I saw the Re-Index option on that screen so I clicked on it, the status light on the player went to yellow and good awhile later it went back to blue saw the total number of songs on that player and everything is fine now (have over 51,000 songs in the Library).....so to my question....

I always thought that the Library (or songs in the Library) were all stored in the Vault and when you used one of the players and looked at the library you were looking at the "list" in and/or via the Vault while it is connected to it....   So does a "list" or a "copy" of the song list (not the actual tracks themselves) in the Library also reside in each player?

Thanks