Having lived in Kentucky, Ohio and now Michigan, I have had 'dumplings' fixed all ways. Depending on my 'cravings' at any given time, I have to say, I like them all. My favorite at the moment is the slick, slippery, rolled dumpling. I distinguish dumplings from noodles (which I handmake, also) by the ingredients and preparation. This is my take on the different types: Noodles
: Egg yolks and water added to flour mixture, usually no leavening. Rolled very thin, lightly floured and cut into slender strips, then allowed to partially or completely dry. I like mine partially dry as this uses less broth (you can end up adding broth all day long to dry, homemade noodles!). Rolled Dumplings:
No egg yolks or eggs added. Large egg-size amount of shortening (to every four cups flour), water and/or milk added to flour, very small amount to NO leavening. Rolled 1/8 to 1/16 inch, floured and cut into small/medium square or diagonal shapes, not allowed to dry. In a pinch, I have also used thinly rolled out canned biscuits, but these become more fluffy than the homemade ones. Fluffy Dumplings:
I believe No eggs should be added to any dumpling rolled or dropped, but some recipes call for egg. I think any extra protein in the dumpling causes them to become tough. Also, a flour with less protein, like cake flour, produces a lighter, fluffier dumpling. Shortening and leavening (I sometimes use self-rising flour) are a must and buttermilk or milk. Dropped by mounded tablespoonfuls or shaped into small egg-sized balls into hot, simmering broth. Allowed to float to the top and simmered covered. Never boil dumplings, they either fall apart (fluffy dumplings) or toughen (rolled dumplings). In a pinch, I have used unrolled, cut into fourths canned biscuits, which become almost as fluffy as homemade.
I have also heard of adding cooled broth instead of milk or water, which may add extra flavor, but I have never tried this. Seems that broth would add extra protein and produce a tougher product, but I'm not sure.
This is just my experience and may not be the opinion of others.