The Web of Things (WoT) is a computing concept that describes a future where everyday objects are fully integrated with the Web. The prerequisite for WoT is for the "things" to have embedded computer systems that enable communication with the Web. Such smart devices would then be able to communicate with each other using existing Web standards.
Considered a subset of the Internet of Things (IoT), WoT focuses on software standards and frameworks such as REST, HTTP and URIs to create applications and services that combine and interact with a variety of network devices. So, you could think of the Web of Things as everyday objects being able to access Web services. The key point is that this doesn't involve the reinvention of the means of communication beause existing standards are used.
Internet of Things is more often used in the context of radiofrequency identification (RFID) and how physical objects are tied to the Internet and can communicate with each other. Both terms are difficult to define precisely, although they are related in their general theme.