Service design is a growing professional practice that aims to develop new or improve existing services. In this context, a "service" is thought of as any combination of customers, users, products and business infrastructure.
Service design investigates and maps out how these components interact with each-other via tools such as a "user journey map" or "service blueprint." These tools allow designers to work with clients to better problem solve and innovate their projects or businesses. In an increasingly service-based economy, the quality of a service experience often determines the actions of customers.
Design research is a term that can mean different things to different people, depending on their profession. In general, it describes a variety of multidisciplinary investigative practices that aim to add value to the design process by emphasizing the importance of understanding the people (users) you are designing for.
An example of when design research is when a design team is trying to develop a solution for a certain group of people. People that are deemed representative of that group are recruited and invited to participate in a series of activities that aim to better their needs and desires. Insights gathered from activities help refine research questions, and ultimately design prompts. The prompts frame concept development and keep ideation tied to real people.
What separates design research from other types of research is that it is not typically meant to be exhaustive or stand-alone, but rather to fuel a creative development process.