A kinematic frame of reference is a mathematical method to determine the position of points in abstract 3D space and scalar time. An inertial frame of reference is a physical method to measure the position of bodies in physical 3D space and scalar time. The latter is often envisioned as three mutually-perpendicular rigid rods attached at a common placepoint, or a lattice of such rigid rods. In addition, there is envisioned a clock at every node of the lattice, which are all synchronized, which requires a method to synchronize them. The common placepoint is called the origin placepoint.
Such a frame of reference assigns coordinates in 3D space and 1D time to every event.
A kinematic timeframe of reference is a mathematical method to determine the position of timepoints in abstract scalar space and 3D time. An inertial timeframe of reference is a physical method to measure the position of bodies in physical 3D space and scalar time. The latter may be envisioned as three mutually-perpendicular rigid monorails attached at a common timepoint. More fully, a timeframe of reference is a system of orthogonal rigid monorails with a regular succession of small, virtually frictionless monorail vehicles in uniform motion (think mag-lev). Such monorails record their location at every node. The start of monorails leaving the common timepoint is the origin event.
Such a timeframe of reference assigns coordinates in 3D space and 3D time to every event.
