My two cents
Focused on intangible
Product design works on what’s tangible both if the product is physical, like a chair, or digital, like a website. Service design tries to design the intangible stuff: the interaction between humans and organisations and the experiences
Taking into account the backstage
Service Design puts a lot of emphasis on taking both care of how things feel for the user and how things are made the backstage (the processes, the employees, the stakeholders, etc).
Thinks about the full journey
Service designers try to think about the full journey someone goes on and don’t focus on just one interaction or product. In a perfect world, service designers even think about the services and interactions that come before and after the service they are building in order to create smooth transitions between them. Some product designers can have a tendency (which service designers also sometimes have) to only be focused on the thing they are paid to improve and not realise that this product is part of a more complex journey.