The reference system that moves rectilinear and uniform is inertial and the reference system that moves rectilinear accelerated, circular uniform or circular accelerated is non-inertial. As I have written before, during the circular movement, even if the mobile is moving uniformly, there is normal or centripetal acceleration because the acceleration vector changes its direction constantly. Just the module remains constant.
The acceleration vector, like any other vector, is decomposed by the parallelogram rule (or triangle rule) in two vectors: tangential acceleration and normal or centripetal acceleration; the acceleration vector is the diagonal of the parallelogram. The tangential component of the acceleration vector, as the name shows, is always tangent to the circular path, so it never changes its direction.
Regarding to inertial or non-inertial referential, at theory of relativity and the consequences arising from here (appearance of the inertial forces for non-inertial observer, the variation of lengths, time, and space etc), all these are just impressions for observers that are in different inertial reference systems and which observe phenomena that take place in other referential systems (which are moving faster/accelerated than the first ones).
The inertial force appears in non-inertial references (so, in accelerated systems), it is noticeable for observers that are in these systems, non-existent for inertial observers, and is a consequence of the acceleration vector. Exactly like all forces in universe exist in pair, the same, for any vector there is another vector equal in modulus and of opposite mode.