It is hard to say that one is because of another, but one thing for sure is that both of these symptoms are cause by the same factor, which is the increase of blood sugar concentration. To make the explanation easier to understand, I will use the term sugar concentration instead of osmotic pressure to explain the movement of water in your body.
The inner world of human body is full of membranes that separate the cells, the tissues, and the organs. These membranes serve as the guarding gates that control what goes in and out of each zones of the body and it is through the controlling of the concentration of minerals in the blood that the body determine how much water stays in the blood and how much should be excrete out.
When someone has diabetes, be it Type I or Type II, his or her body loses the ability to control the sugar content in the blood and this results in the increase of glucose concentration in the blood. When the glucose concentration is high in the blood it will 'absorb' the water from the interstitial fluid (the part between blood capillary and the cells) in order to balance up the concentration between these 2 parts of the body. This will eventually cause the body cells to lose water in to the bloodstream and it is the dehydrated cells that send out Thirsty signal to the brain.
Now come to the kidneys. As soon as the blood enters the nephron (smallest processing unit) in the kidney, almost all the fluid and (and the dissolved substances) are the blood is sieved out into the urine tubules. And then the re-absorption process takes place where the nephron reabsorbs the useful nutrients together with water back into the bloodstream.