The two senses of this word seem very different. One sense is just another way to say like, and the other is an adjective describing the state of being divided into different portions. I can't see immediately how they are related. How did the antecedents of this word evolve? What is the etymology?
According to the New Oxford American Dictionary, both come form the late Latin partialis (part), but through different Old French words: from partiel in the meaning of “incomplete”, and from parcial in the meaning of biased.
Etymonline does not corroborate this, but it indicates that the meaning of “incomplete” emerged later than the meaning of “biased”.
These are two different meanings of the same word:
partial |ˈpär sh əl| adjective
1 existing only in part; incomplete : a question to which we have only partial answers.
2 favoring one side in a dispute above the other; biased : the paper gave a distorted and very partial view of the situation.
That's from NOAD. Their example sentence in the second meaning I don't think is unambiguous enough, so I would rewrite it as: the paper gave a distorted view of the situation, one that was partial to the incumbent mayor's party.