At the technical level there is no real difference.
The difference is instead on an organisational level: a qualified trust service provider must adhere to specific requirements like making sure that the information in the certificates including the times are correct, that certificates will be quickly revoked if necessary and that it is kind of impossible for an attacker to create its own certificates. For more details see Wikipedia:Qualified digital certificate:Role of a qualified trust service provider.
The idea behind this requirements is that the issued certificates are sufficiently trustable in order to be used for digitally signing various kinds of data in the context of public and private transactions. Sufficiently trustable means that when in doubt a court will accept the digital signature as proof, which means that it needs to be sure that it could not have been faked by an attacker.