Digital systems covers a wider market that embedded systems.In other words embedded systems are a type of a digital system.A embedded engineer must have knowledge and skills in both hardware and software.
Real time skills and best practices must be followed by an embedded engineer.A digital engineer May not need to go that deep.Of course a digital engineer may become an embedded engineer.
It’s a mater of specialization and dedication.
The terminology is not standard, however I imagine that the embedded systems engineer will need to work in both hardware and software, perhaps mostly in software, while a digital systems engineer might work more in hardware.
If you have both hardware and software skills, you should be able to work in embedded systems.