Some people think design is a subset of engineering. According to this mindset, the goal is to make a thing of some kind. Engineering figures out how to make the thing, and design figures out how to make that thing more appealing to people.
Others think engineering is a subset of design. According to this mindset, the goal is to improve peoples lives. Design figures out what people are doing, what they need and what is required to make their lives better, and engineering figures out how to make those things happen.
Engineering creates systems. People from outside the system use the engineered system.
Design creates systems made up of people and things. The people who use the system are a part of the designed system.