Currently, there are two main versions of Chinese used around the world - Simplified Chinese (CHS) and Traditional Chinese (CHT). The geographical areas that each of the versions covers are as follows:

Simplified: China and Singapore
Traditional: Taiwan, Hong Kong and overseas Chinese communities

In the computer realm, Simplified Chinese uses GB2312 encoding and Traditional Chinese uses the so-called Big5 encoding. They have different Windows, Mac OS's and application software. Technical terminology and the way people speak about them are also quite different. Translation departments of large corporations, therefore, treat the two versions as two different languages and typically have different teams of people handling each of them.

Mandarin or Cantonese
Mandarin or Cantonese is a dialect of the Chinese language, not a written language and should not be used when requesting written translation, though it is quite correct to use them if you are looking for an interpreter. When these terms are used to denote a written language, however, they can easily cause confusion or misunderstanding. You also run the risk of getting the wrong version. For example, Mandarin is spoken both in China and Taiwan, and increasingly in Hong Kong. Many people in the US Chinese community also speak Mandarin. When a client from Taiwan requests Mandarin translation, s/he is actually asking for traditional Chinese. If a project manager from a US agency asks for Mandarin translation to be used in Mainland China, what s/he wants is Simplified Chinese. Therefore, the best way is to verify the target region, then offer the correct version from the above list and ask the client to confirm. This way, you will never end up with a wrong version.