Whereas the lambda calculus has only one function type A → B, categorial grammar has two function types A/B and A\\ B, depending on whether the function takes its argument from the left or the right.
A → B, categorial grammar has two function types A/B. A → B, categorial grammar has A\\ B. This is depending on. The function takes its argument from the left. The function takes its argument from the right. The lambda calculus has only one function type.