Translaminar implies the breaking of fibres, whereas inter- and intralaminar refers to whether the cracks grow in between the plies or through the thickness, respectively.
The main difference between the two modes of fracture toughness is when they are used. The interlaminar value is the relative resistance of the composite to crack growth along the interface between adjacent laminae - growth in the direction of the fiber length. Because most scenarios for the use of composite materials involve stress configurations that produce localized stress concentrations localized in regions such that the fiber stiffness is not involved, resistance to growth of damage through the thickness becomes relatively unimportant. All substantial loading components, although referring to certain modes of delamination, are multiaxial which would allow mixture of different responses of the composite plies with standard sandwich theory.