The genetics of diabetes are very complex, but before I delve into that, you need to be aware that the terminology has changed. What used to be called Juvenile Diabetes is now called type 1. What used to be called Adult Onset diabetes is now called type 2, as you note. The reason for no longer using the terms Juvenile and Adult Onset is that both Juvenile and Adult Onset Diabetes occur throughout the life span. Thus, the old terms are misleading.
Type 1 and type 2 are completely different conditions which share a common clinical end result, elevated blood glucose levels. Actually type 2 and 1 are really families of diseases, but we'll leave that complication out for simplicity's sake.
Yes, diabetes of both types can run in families and there is a genetic component to the diseases which may, or may not, be inherited. On the other hand, the majority of diabetics, of either type, do not have a first degree relative with the disease. The genetic predisposition to diabetes is fairly easy to come by. In both cases, there are probably many contributing genetic locations and the probability you will get the disease depends on which subset of the locations that have the disposing characteristic a particular individual winds up possessing. There also appear to be some genes which protect from the disease. The general picture of the onset of diabetes is that you have a genetic predisposition which is then triggered by some environmental factor. Beyond this very general picture the two types start becoming distinct.
The probability that an individual with a type 1 sibling will develop type 2 diabetes is the same as in the general population, since they are independent conditions. The estimates of the risk of type 2 vary quite a bit for a couple reasons. Type 2 incidence rises very steeply with age and so any age cut off in your sample has a dramatic effect on the cumulative incidence. Rates also vary widely depending on the details of the population you look at. Lastly, much of the type 2 diabetes remains undiagnosed, so your calculated rate depends heavily on your estimate of the undiagnosed population. In round numbers, the risk of being diagnosed with type 2 diabetes during a 70 year life is 10%. The risk of contracting type 2 is close to twice that.