What causes the texture difference between Greek style yogurt and regular yogurt? In the US, Greek-style yogurt and regular yogurt are both made with cow's milk, yet they have a distinctly different texture. 

When I described the texture of Greek yogurt to my nutritionist, she used the word "pithy". It, to me, feels like a thin layer of fuzz (like the skin of a peach) gets left on the surfaces of my mouth when I eat it.

Initial thought would tell me that it's because Greek yogurt has less water in it, but I made some homemade yogurt last weekend, using Greek yogurt for a culture, and despite being quite thin, it still had that pithy texture.

What gives Greek yogurt this texture? Or, what makes regular yogurt not have this texture?
I would describe it as an almost chalky texture. Greek yogurt is typically strained 3+ times before packaging and in most cases is made from dairy with a higher fat content. The tang and texture are due to the whey being almost completely removed from the yogurt. The higher milk serum content (whey) in US yogurt makes it sweeter and obviously less viscous.