North is an Noun, adjective and adverb. Northern is only an adjective. Describes something that comes from the North or is in the North. So you could say "North China is colder than South China." And "Northern China is colder than southern China." As they are both adjectives. But you could not say "Many rivers in China come from the Northern." As Northern is not a noun. "Many rivers in China come from the North." As North is a noun. Or "Many rivers in China come from the Northern/North regions." Both being used as an adjective for the word regions. I think :)

North China would be understood as a specific place -- I don't know if in fact it is defined -- with definite boundaries which may be officially specified or at least customarily understood. Northern China would mean the area of China towards the north, but the exact area would depend on the context and the attitude of the speaker. Let me give you another example, which might make the distinction clearer. South America is the continent. Southern America would mean the part of America towards the south, so if you normally take America to mean the US (which many people do), then southern America would represent the southern part of the US. An entirely different place! (To be fair, though, I think most people would say "the southern US" in this context.) Also, note that "north" etc. can also function as nouns and adverbs, whereas "northern" etc. are strictly adjectives.