Chinese and Mandarin are essentially the same thing how people refer Chinese these days, but you don't write Mandarin.
Chinese is the written version of the language. Mandarin is the spoken language, it is the pronunciation of the words. Cantonese, Hakka and Mandarin are the speaking language. Each one is different enough that you can't really understand each other, well, a couple of them you can.
Written down they are all the same. Simplified Chinese are if you are in China, but all the Chinese that has immigrated from China in the past 50 years are mostly from Hong Kong and thus writes Traditional Chinese.
So, in the west, if you want to translate into Chinese, chances are is traditional Chinese.
If you are trying to get a job in China however, then you want simplified Chinese.