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.
Non single diffractive are Double Diffractive and No Difractive, Some no Diffractive are MB as coment, here some interesting link http://school-diff2013.physi.uni-heidelberg.de/ now the link of the 2015 school http://school-diff2015.physi.uni-heidelberg.de/