Without going into too much detail, the main difference is how much privileged access Google has to your phone.
On Stock, Google Mobile Services (GMS) apps that are included in the factory image have system-level privileges. If you look at many of GMS apps' permissions, they have virtually unlimited access to everything on your phone, including access to read all your files, change your settings, install other apps, log some aspects of your app usage, etc.
Armed with that info, I think it's best to read this section on the website to know more about how Google Play apps work on GrapheneOS: https://grapheneos.org/features#sandboxed-google-play
A tl;dr of that page is GrapheneOS works without Google Mobile Services (GMS) apps. They're all restricted to the same app sandbox as other apps and have no special permissions.