A frame of reference is an object used to measure the dynamical properties of another object, while a coordinate system is a tool for visualizing and analyzing vectors. Although all reference frames can be represented by coordinate systems, they serve different purposes; reference frames focus on kinematics, while coordinate systems facilitate algebraic analysis. A rotating frame of reference is indeed non-inertial, but it can still be represented by a coordinate system. The discussion highlights that while they are closely related, a reference frame does not necessarily require a coordinate system for its definition. An example of a coordinate system corresponding to a rotating non-inertial reference frame is requested for further clarification.