BelM's thread about how you tell where you're from got me to wondering. We normally divide verbs into transitive and intransitive verbs, but the transitive verbs really come in two different types: those that take merely a direct object and those that take both a direct and an indirect object. Is there a grammatical term that distinguishes between those two types?

Edit:

Dr. Bill suggested I give an example of the two types of transitive verbs: I can read a book, but I can't just give a book, I have to give someone a book. Even in my opening sentence in the edit there was an understood y'all between give and an example.