Plesiotwins and diperiodic twins have in common the fact of being characterized by a low degree of lattice restoration. Plesiotwins differ from twins by the fact that the relative orientation of the individuals is obtained by a non-crystallographic rotation about the normal to the composition plane, whereas for twins this rotation is crystallographic, apart from possible small deviations coming from metric pseudosymmetries. In the case of plesiotwins, the low degree of lattice restoration comes from a large coincidence site lattice (CSL) in the composition plane. Diperiodic twins, instead, have a small CSL in the composition plane but the second plane of the same family contributing to the overall lattice restoration is too far away from the composition plane to be considered significant. It is shown that plesiotwins can occur as reflection twins if the composition plane is not parallel to the twin plane, and as rotation twins in the case of parallel hemitropy. Diperiodic twins can in principle occur in any category, but either the metric conditions to obtain a diperiodic twin are actually in contrast with the metric pseudosymmetry required for twinning or the result is actually a hybrid twin. This justifies why no confirmed examples of diperiodic twins are known to date.