What is the distinction between inertial reference frames and those differing only by a translation or rotation of the axes?

One can distinguish the inertial frame of reference against the translation of the axes when the translation or rotation occurs non-uniformly.
If the translation of one frame of reference relative to the other is such that observer in one frame measures some acceleration of the other, then the observer can draw a distinction between his frame and the inertial frame of reference.
It is important to note that the rotating frame will always be non-inertial because to account for the rotation there must be a change in velocity vector. Therefore the inertial reference frame will always be distinct from the rotation frame.
However the translation can be distinguished from the inertial frame of reference only when the translation occurs at a uniform velocity.