All games will be BC on Neo, but beginning in October all PS4 games released must have a separate Neo executable that runs at a native resolution of at least 1080p and performs as well as or better than the PS4 classic code. So basically the same disc will work in both consoles, but if you stick it in a Neo it'll run a different exe. Devs can patch their games released prior to that to also support the special Neo mode, but if they don't it'll just run it in the regular PS4 classic mode.
*Edit - Link to my post in the PS4 thread where I explained it better and more fully.