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I saw these two words, which I had always assumed meant the same thing, in the same sentence (below). It begs a question as to the difference between them:
Sentence:
This restless and perpetual change, as inexorable and unstoppable as the waves and tides, implies a world in which all human actions necessarily have uncertain effects.
Inexorable means unresponsive to entreaty, or unrelenting. In other words, you can ask the waves and tides to stop, but they won't. In addition, the connotation is that the effect is a negative one--an inexorable decay.
Unstoppable has no such personification aspect to it, and its effect is not necessarily negative. You could have unstoppable fortitude.
It's a good example of how semantic shift takes place. The two words are arranged as a sort of duplication, and in a sense, they do. This duplication emphasizes the meaning of either word. Great.
But they don't always mean the same thing, as pointed out above. So near-synonyms or sometime-synonyms are taken by a hearer as identical in content or interchanged inappropriately. Thus, inexorable comes to be used as "unstoppable" when it means "can't be exhorted," which isn't exactly the same thing - after all, perhaps a stubborn mule refuses to be exhorted into movement, that is, to start. In point of fact, though, we'd all think it was strange if we heard about the inexorable mule refusing to start.
