Buckling and yielding are completely different concepts.
Buckling occurs when an elastic structure does not move back to its initial position as long as the load is applied. Buckling is a purely elastic phenomenon. When elastic material is subjected to a small load, the deformation is usually small as well. This is different with buckling. Buckling requires a significant load in one direction, but then a very, very small load in a perpendicular direction can lead to destructive deformation (depending on the amount of deformation allowed by the system). Buckling is a stability problem, and the sample geometry is essential.
Yielding occurs when the behavior of the material itself changes (due to the high load). When a material yields, the relative position of the atoms change.
Edit: To realise the 'very, very small load' in perpendicular direction it is usually sufficient to apply the large load not perfectly in line with the stability axis. Since buckling is a stability problem, the large load leads to an instable system in the first place. In order to actually deform, some initial deformation in perpendicular direction is required which is then amplified.
I also slightly changed the first sentence of the buckling paragraph to account for Wasabi's comment.