The term centrosymmetric refers to a space group which contains an inversion center as one of its symmetry elements i.e. for every point (x, y, z) in the unit cell, there is an indistinguishable point (-x, -y, -z).

Out of these 21 point groups, except group 432, crystals containing all other point groups exhibit piezoelectric effect i.e. upon application of an electric field, they exhibit strain or upon application of an external stress, charges develop on the faces of crystal resulting in an induced electric field.

Out of these 20 non-centrosymmetric point groups, 10 belong to polar crystals i.e. crystals which possess a unique polar axis, an axis showing different properties at the two ends.  

These crystals can be spontaneously polarized and polarization can be compensated through external or internal conductivity or twinning or domain formation.

Spontaneous polarization depends upon the temperature. Consequently, if a change in temperature is imposed, an electric charge is developed on the faces of the crystal perpendicular to the polar axis. This is called pyroelectric effect. All 10 classes of polar crystals are pyroelectric.

In some of these polar non-centrosymmetric crystals, the polarization along the polar axis can be reversed by reversing the polarity of electric field. Such crystals are called ferroelectric i.e. these are spontaneously polarized materials with reversible polarization.

So by default, all ferroelectric materials are simultaneously pyroelectric and piezoelectric. Similarly, all pyroelectric materials are by default piezoelectric but not all of them are ferroelectric.