A “dialog state tracker” is like a hypothetical device, or more accurately a component, representing an unsolved problem.
An SLU (spoken language understanding) system means to me an acoustical device that interfaces with, or translates to, a textual NLP (natural language processing) engine. However, “language understanding” is also an unsolved problem. The acoustic part is essentially solved; it’s the NLP understanding part that is not solved.
A “dialog state tracker” represents an additional component within this ecosystem. Essentially, a “dialog state tracker” would link the present with past and future dialog states, in other words keeping the darn thing on topic across time.
See also my Quora answers to: