No not the exact same as Xbox.
If your PS4 or PS5 is set as primary console, you can disconnect it from the internet, install and play any offline games from Disk and also play any digital title you downloaded from the store. That is not the same for Xbox where in some cases you need to connect to the internet to authenticate before you can play a game you installed from a Disk and some Digital titles even when the console is set as home console. Thats not how it works on PS4 or PS5. Smart Delivery titles have to be connected on the internet to install and play, not the same on PS5.