This incompatible use of the term "fictitious force" is unrelated to non-inertial frames. These so-called "forces" are defined by determining the acceleration of a particle within the curvilinear coordinate system, and then separating the simple double-time derivatives of coordinates from the remaining terms. These remaining terms then are called "fictitious forces". More careful usage calls these terms " generalized fictitious forces " to indicate their connection to the generalized coordinates of Lagrangian mechanics. The application of Lagrangian methods to polar coordinates can be found here.