The class of languages characterizable by these formalisms fell within the requirements of what Joshi (1988) called "mild context sensitivity" (MCS), which proposed as a criterion for what could count as a computationally "reasonable" theory of natural languages-informally speaking, that they are polynomially recognizable, and exhibit constant growth and some limit on crossing dependencies.
the MCS class is much much larger than the CCG/TAG languages, including the multiple context free languages and even (under certain further assumptions) the languages of Chomskian minimalism, so it seems appropriate to distinguish TAG and CCG as "slightly noncontext-free" (SNCF, with apologies to the French railroad company).