For my final resource project in my senior year of high school, I was researching the Wenzhou dialect, a dialect of Chinese spoken in the vicinity of Wenzhou, a city in southeast China.
A map of the primary branches of Chinese. The Wenzhou dialect is a Wu dialect.
By Map_of_sinitic_languages-en.svg: Wu Yue (original); Gohu1er (SVG) derivative work:
Kanguole (Map_of_sinitic_languages-en.svg)
[CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons
The terms "Wenzhou dialect", "Wenzhounese", and "Wenzhouhua" are all synonyms; however, they have two meanings. In some cases in this anthology, the broad definition is used, referring to the local dialects of Chinese spoken within the borders of the prefecture-level city of Wenzhou, including the city of Rui'an, and some related dialects in nearby areas; this would include the Rui'an dialect. The narrow definition refers specifically to the local dialect spoken within the actual city of Wenzhou.
The "Rui'an dialect" and "Rui'anhua" are likewise synonyms, referring to the dialect spoken in Rui'an.
Rui'anhua and Wenzhouhua are how those dialects are referred to, as pronounced in Mandarin Chinese. I don't think those are the official terms if we are to discuss them in English. I use them sometimes anyway.
"Hua" (话) means "language" or "speech" in Chinese. It is pronounced as a single syllable, "hwuh."
"Rui'an" (瑞安) is approximately "ray un."
"Wenzhou" (温州) is approximately "when dzhoh." Sorry about the "dzh" - there's no concise way to describe it; the "zh" sound doesn't exist in English.
"Mutual intelligibility" is defined here.