Electrostriction is a property of all electrical non-conductors, or dielectrics , that produces a relatively slight change of shape, or mechanical deformation, under the application of an electric field. Reversal of the electric field does not reverse the direction of the deformation.

The converse piezoelectric effect occurs only in a particular class of dielectrics.

Electrostriction - The change in the dimensions of a body as a result of reorientation of its molecules when it is placed in an electric field. If the field is not homogeneous the body will tend to move; if its relative permittivity is higher than that of its surroundings it will tend to move into a region of higher field strength. (Compare with magnetostriction.) source: Oxford University Press, "mini dictionary of physics 1988"

Right. Here be the straight dope. ( Source - IEEE handbook, among others).

Electrostrction is a property of all dielectric materials. When an electric field is applied to a dielectric, it develops polarization(s). It then deforms, and the strain (ratio of deformation/original dimension)is proportional to the square of the polarization, in the simplest sense.

MOre formally, the electrostriction coefficient is a fourth order tensor (Qsubijlk), relating second order strain (xsubij) and first order polarization tensors (Psubk, Psubl).

xsubij = Qsubijkl * Psubk * Psubl

Piezoelecticity is NOT the converse of electrostriction. Perish the thought. It is a LINEAR effect, compared to the QUADRATIC electrostriction effect. In this linear property, the third order Piezostriction coefficient linearly relates second order strain and first order polarization. It is apparent only in materials without a centrosymmetric crystal structure. Because of the linearity, it is perceived as easier to work with, even though 'walk-off' errors in Piezostriction are significantly larger.

xsubij = PIsubijk * Psubk

Give yourself a brownie point or two if you figured out that you can make an electrostrictor piezoelectric by biasing it with a permanent polarization!