"Zeppoles" or traditional Italian fried dough is made with pizza dough. It's a thick dough that's pulled by hand and tossed into hot oil. Once it is golden brown, it's quickly removed. It's a chewy treat. Some people like it topped with powdered sugar, some chocolate, and many people like it plain.
"Funnel Cake" is a thin quick bread recipe that is very liquidy. It is poured into hot oil and quickly turns golden brown. Typically, by the time the pour is made, there is only a minute or so until the whole thing must be flipped to brown the other side. When it's done, it's then usually sprinkled with powdered sugar and/or cinnamon, and may be topped with ice cream or chocolate sauce or some kind of fruit.
Beignets are a yeast raised donut. They are rolled and cut, then dropped into hot oil to give them their characteristic puffy pillow shape. Upon their exit from the fryer, they are covered in powdered sugar.
The only thing that all three of these have in common is the powdered sugar and the ability to eat them with your fingers. Beyond that, they are completely different.
