Cue one thousand years of people trying to say
rødgrød med fløde.
As for the 言語 (yányǔ) - 方言 (fāngyán) distinction, I have a link that might be of interest. 言語, iirc, typically refers to spoken language, specifically, as 言 (yán) as a character generally refers to words or speech. This contrasts with words like 中文 (zhōngwén), which refers to written Chinese, or even more generally 文字 (wénzì), which refers to written language or a particular script.
方言 on the other hand can be decomposed as meaning "regional speech" or "local speech." For this reason, Victor Mair prefers the use of the term
topolect. It's a term that's both more and less specific than the word "dialect." On one hand, it refers specifically to the spoken language used in a specific area. On the other, it doesn't specify the size of the area or even the relationships of the language to each other—the word 方言 has been used to refer to not just different Sinitic languages but also languages like Japanese, Korean, and Vietnamese. If we try to translate 方言 as "dialect", we obviously run into a problem as these are clearly not dialects of anything, let alone of Chinese—but translating 方言 universally as "language" is equally problematic, since we can talk about the 方言 of Shanghai, which is not generally considered to be a separate language within Wu. "Topolect" splits the difference by just referring to it as "the speech of a particular region".
This about covers it, and is part of the reason why the "language/dialect" division works so poorly. In the Chinese languages, these difficulties are compounded by less dialect levelling (at least historically, and there's that word again!) and the lack of the aforementioned cutting tool of writing—without an alphabetic standard (at least until pinyin), characters were all pronounced in local ways to a greater or lesser degree of mutual intelligibility with the other topolects.