I lived in China for 11 years and learned some Chinese cooking while there. Dumplings of various sorts are found all over China. The ones we call potstickers, if made at home in the North, are the exact same as jiaozi, the water boiled ones. It does just depend, as one poster said, on how you cook them. If bought at a street stall, however, there is another type of pot sticker that is open at both ends and couldn't be boiled.
The trick to boiling handmade, closed Chinese-style dumplings so they don't open up is to bring the water to just under boiling, put in a batch, then when the water wants to start boiiling again, add one small bowl of cold water to bring the temperature down. They will do this one more time, then when the water comes to a boil the third time, the dumplings should be done.
There are many kinds of fillings you can make. My favorite is the same as the poster from Shanghai's, and is a very standard one: ground pork, Chinese cabbage, scallions, and ginger (and a little bit of soy sauce and sesame oil). But another good one is with ground beef and carrots, also scallions and ginger in there. In the north, they usually put jiucai, a strong garlic grass, in the pork ones. It's okay...everyone seems to love that filling but me. I guess I just love the above pork one more. Once in a while I make the pork ones from scratch, wrappers and all, but it's very time consuming. I have a Chinese friend in New York City who makes pot stickers using Pillsbury biscuit dough. They're tasty, but you can't eat as many of them; they're too heavy to have more than a couple of.
Usually making jiaozi is a social affair in China. You invite friends over to do it with you. You make up the fillings, perhaps two or three kinds (probably a pork filling and one with shrimp), and the wrapper dough in advance, then when your helpers/dinner guests have arrived, you work together rolling the dough into little circles and filling them. When they're all wrapped, trays and trays of them, you start boiling them.
I'm living in Korea now, and they put that (rice? sweet potato or mung bean starch? I forget now) translucent vermicelli, cooked and chopped up small, in their potstickers, with hmm...what else? sometimes tiny bits of chopped up firm tofu, sometimes a little scrambled egg. And minced leeks, and pepper (black).