Three versions of Chinese Characters

There are (at least) three versions of Chinese characters:
We have 'traditional characters' (Mainly used in Hong Kong, Macau and Taiwan, sometimes in Korea and Mainland China) [=T],
we have 'simplified characters' (Mainly used in Mainland China and Singapore) [=S]
and we have 'japanese simplified characters' (used in Japan) [=J]

Example: These characters are the same but appear in three different versions:
T: 兩 (liang3 – two; both)
S: 两 (liang3 – two; both)
J: 両 (ryou – two; both)

Japanese call "their" chinese characters 'Kanji' [=J]
Chinese call them 'Hanzi' [=S,T]
Korean call them 'Hanja' [=T]

If you learn chinese choose between T and S, or learn both versions. I recommend to learn T actively and S passively because it's easier to read S after having learnt T than vice versa.
(*learning actively: afterwards you can both – read AND write the character;
learning passively: you learn only to read the character, but not to write it)

And of course because it's easier to make mnemonic rhymes tor T than S.
(I believe that “simplified” characters are not necessarily simpler than T!!! … )

If you want to know more about the differences visit this wikipedia link.