My two cents
ITIL Service Design is focused on the creation of IT services.
Service Design as championed by the Service Design Network can be applied to any service.
Digital services. But also physical services and services that are all in between and mix things together.
Therefore ITIL is much more technical and focused on the IT stuff.
Where Service Design, is much more holistic and comes more from a design perspective rather than a technical, an IT perspective.
I don't see these approaches as opposing but rather as being complimentary.
Obviously take everything I say here with a grain of salt, as I'm, as service designer who is also part of the Service Design Network. And I'm definitely not an it guy.
Resources to go further
Here a few selected resources about ITIL Service Design to go further:
A description of the ITIL Service Design Process