How is the Kanji character 豚 related to the chinese 猪 / 豬
豚 is pronounced tun2 in Mandarin and tyun4 in Cantonese.

The only word I know which still uses it is 海豚 hai3tun2 "dolphin". The Japanese reading is ton (on), buta (kun), as I'm sure you know.

豚 was the original character (with the meat radical on the left hand side), while 猪 meant a wild pig (which is suggested by its radical). Japanese borrowings from Chinese happened in waves, as the Chinese language itself changed. Characters which were later supplanted in Chinese were fossilised in Japanese, because they were still current at the time they were borrowed. 

This is why Japanese uses characters like 足, 食 and 寝 which have fallen into disuse in modern Mandarin, or lost their identity as free morphemes, or have gained different meanings.

Semantic and lexical divergence from Mandarin is of course also present in Chinese topolects. Hokkien for example, preserves the classical character for chopsticks, 箸, which is also still the preferred form in Japanese rather than 筷. Also, see on the same page that 册, whence chaek in Korean, is still current in Hokkien too.

[1] http://weizhoushiwang.blogbus.com/logs/418660.html