Non Single Diffractive (NSD) events are actually the sum of Non-Diffractive (ND) and Double Diffractive (DD) events

In diffractive events an incident particle is excited. A so-called diffractive system is created that carries the quantum numbers of the respective incoming particle (except possibly the spin). Subsequently it evolves and decays.

Non-diffractive collisions have many particles in the central region, steeply falling to higher rapidities.

In a single-diffractive collision only one of the beam particles breaks up and produces particles at high rapidities on one side. 

In a double-diffractive collision  both beam particles break up and produce particles at positive and negative high rapidities.

Thank you very much, Ijaz Ahmed and Imtiyaz Rather !