How to install games on PS4

From the question, it may not be entirely clear, I'm interested in this, when I bought ps4 from my hands, there were games on it already on hard, some of them stopped working in bulk, like the license ended, but some still work, ps + I never had. I also bought some games in the ps store, from my account, as I understand it, and all games are available in the library. I just don't understand, is the game downloaded from psstor tied to an account or to a console, is the psstor account itself tied to a specific console? If, for example, I sell a console, but I don't want to sell games, can I log out of my account and log in from another console and install them for free. And how then do games from the previous owner work for me, and I already have my own account, she's not tied to anything at all, and without a full disk, the license works only after buying in psstor, as I understand it,