On Wikipedia, buckling is defined as follows:
In engineering, buckling is the sudden change in shape of a structural component under load such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have buckled.
Why do we define buckling as a sudden change in shape? This definition implies that a column is perfectly straight until we apply a load over a critical limit, after which the column suddenly curves sideways. But in real life, columns are not exactly straight and loads are not applied exactly to the center lines of columns so there is a bending moment on the column (and therefore everywhere in the column) for any load, not just a load above a certain limit.
Classical Euler buckling assumes a perfectly ideal column, and for that buckling appears as a bifurcation solution after a critical load is reached (and not before), but a real life column is not ideal and any eccentricity on the column or the load means that a bending moment is technically present for any load, however small.
So are real life instances of buckling not strictly speaking buckling according to this definition?