There is the type that is caused by having one's pancreas removed surgically for other reasons (ask Landileigh about that). That means you make no insulin, but you don't have the antibodies that a Type 1 or Type 1.5 has.
There are several types of MODY. MODY is a monogenetic (one gene) type of diabetes. Some of these genes result in the islets being a bit "slow" and needing mild stimulation from an insulin secretagogue; others have different effects (ask Jenny (Diabetes Update, Blood Sugar 101) about MODY!); each different type of MODY requires different treatment.
There are also conditions that are not necessarily called "prediabetes" but probably should be (or rather, "prediabetes" and "type 2 diabetes" should be called these, in different degrees, as well): impaired glucose tolerance (IGT) and insulin resistance (IR). If diagnosed early, these usually respond to diet, exercise, and oral medications.