What is the difference between the limit of proportionality and the elastic limit?

Limit of proportionality is the end of where Hooke's Law applies. At greater forces, the extension is no longer proportional to the force. From then on the Force extension graph becomes curved. The elastic limit is where plastic deformation starts-i.e the wire no longer returns to the original length when the force is removed. For metals, there is usually a small gap between the two points on the graph-i.e the metal no longer obeys Hooke's law but it will still returns to its original length when the force is removed.

The limit of proportionality is the extension beyond which Hooke's law no longer applies, i.e. the extension is no longer proportional to the force. The elastic limit is the extension beyond which the object will not return to it's original shape when the force is removed. It is possible to be extended beyond the limit of proportionality but not reach the elastic limit.