Elasticity is the ability of a solid to regain its shape after distorting forces are released.
Tensile forces stretch an object. Compressive forces compress an object.
Brittle materials snap without any noticeable yield. Ductile materials can be drawn into wires.
Elastic limit is the point on a stress strain graph where the object will become permanently deformed. Limit of the proportionality is the point at which the material stops following hookes law.