1.这些说法没有任何区别,关键是楼主对south/southern的词性把握尚有欠缺.
2.southern只能做形容词,所以它要修饰名词part做定语,构成固定搭配：in the southern part of China.
但是,绝对不可以说：in the southern of China.
3.而south兼有三种词性：名词,形容词和副词.
1）做名词时,当然就有固定搭配：in the south of China
2）作形容词时,等同于southern,所以以下两种说法都是正确的,即：
in the south part of China = in the southern part of China
3）做副词时,副词south = in/on/to the south（名词） = in/on/to the south/southern（形容词） part.
如：Guangdong lies in the south of China.名词
= Guangdong lies in the south/southern part of China.形容词
= Guangdong lies south of China.副词
最后一个例句中的south就是副词,等同于介宾短语.这句也是考试中经常考查的考点.
4.最后提一点,south作为形容词的用法虽然在语法上无误,但是平时很少用,楼主其实不必过分计较.