I do believe wonton are served in soup, if memory serves me correct. Jiaozi as you can said can be served boiled, or fried, as in the case of cooking japanese style.

Chinese fried dumplings are called 'guotie' (first tone and neutral) but there may be other fried varieties that i don't know about. We should ask our resident Mandarin-fluent posters-SB, Turnoi, O'Shei, what they(if exist) are called hahaha. Wot famous poster said this? "Just cos I grope your knee and leer don't mean you don't have to pay for your own guotie" -Well said, San Migs.