According to Etymonline, history comes from the same root as story. If they are from the same word, where does hi- come from? Is it just because of the English habit of taking names from other languages verbatim or is there something more to it?
If you look more closely you will see that the hi- was there originally, in Greek historia from which it was borrowed into Latin. The initial syllable was weakened and sometimes dropped in Late Latin, and reduced to e- in Old French, from which the word was borrowed into Middle English.
In ME it shows up as historie, istorie estorie and histoire, all representing OF forms, probably influenced by Latin – for of course Latin was still a living written language of learning and scholarship. Alongside these a “native” version, with the initial syllable entirely dropped, began to show up; this appears as storie, stor, storri, with plurals stories, storise, storius, and storien.
All these forms were used indifferently for any narrative account, whether formal chronicle or patent romance. It was not until Early Modern English – the 16th century – that spellings and forms began to shake down– probably, again, influenced by the status of Latin as the principal language of learning – into the contrasting history = factual narrative and story = fictional narrative.
Note that to this day French histoire means both story and history – as does the corresponding term in German, Geschichte. I imagine this is true in many other European languages.
I must also acknowledge that over the past two generations historiographers have grown skeptical of the Rankean eigentlich gewesen and are much more conscious of the element of mythopoesis in their work; so in a sense history is collapsing back into story.