I don't recall that there's much connection between spoken Chinese and spoken Japanese, although it's been many years since I studied Mandarin. I do seem to recall though that the written languages are related--that the Japanese may have adopted the Chinese characters for their own language( based on meaning of words or pronunciation I can't say). What's interesting (I think) is that all dialects of Chinese (Mandarin, Cantonese, etc.) use the same characters, so that no matter what your spoken dialect, you can read any common Chinese writing.
It's pretty difficult to say what the syllable "tai" might mean, unless you have either heard it pronounced (Chinese is tonal) or seen it written as a character.