In the book This is Service Design Thinking1 One of the definition quoting The Copenhagen Institute of Interaction Design is:
Service Design is an emerging field focused on the creation of well thought through experiences using a combination of intangible and tangible mediums. It provides numerous benefits to the end user experience when applied to sectors such as retail, banking, transportation, and healthcare.
Service design as a practice generally results in the design of systems and processes aimed at providing a holistic service to the user.
Then, the same book spells out the constituting fields. I have ordered them roughly based on how much overlap there is between these fields and those in UX:
- Interaction design
- Product design
- Design ethnography
- Social design
- Graphic design
- Strategic management
- Operations management
While you can argue that certain disciplines with UX could cover all these fields, UXers hardly deal with strategic and operational management.
Another way to look at this is that a retail business may hire UX professional to improve their interactive products (internal and customer touch-points), a business aiming to excel on the service front would normally approach service designers.
As others have mentioned, there is no agreement on what UX or SD include or exclude, but the reality is that while they overlap, there are differences.
1 Stickdorn, J.S.M., 1009. This is Service Design Thinking.: Basics - Tools - Cases by Marc Stickdorn, Jakob Schneider (2014) Paperback, 1 edition. ed. Bis Publishers.