Indeed, there appear to be somewhere over 50 genes currently associated with Type 2 and new ones are still being found. The MODYs are a single gene and one of the MODY genes is also associated with other forms of Type 2.
Type 1 has a lower genetic component (from twin studies etc.) but there are distinct clusters in some families involving Type 1 and several other autoimmune diseases, thyroid and rhemuatoid arthritis to name but two.
Thanks to my late aunt's genealogical research I can see that while insulin resistance without overweight is not common in the population it's very common in one line of my family.