Sentinel Hub running as part of Copernicus Data Space Ecosystem has the same set of features as the one running on sentinel-hub.com.
CDSE has free-for-user plans, funded by the European Commission.
The systems, however, are completely detached one from another. You cannot use the API key from one in the another - you need to register on CDSE and get API key there.
Security implications require the authentication and authorization to be separate.
The main difference, for the moment, is the lack of availability of Landsat collections in the CDSE - something that we are hoping to address in the future.