During one of my office hour sessions, I taught about the use of "a" and "an" in non-standard cases. The thing that (apparently) a lot of national curricula fail to teach about English to their students is that English - as much as it is a written language with thousands upon thousands of books - is a spoken language, and that parts of grammar are based on this point.
There really is no difference in the definition of "a" vs "an". The only difference is in the use of the latter when it precedes a vowel sound; not actually when it precedes a vowel (e.g. "an hour is a unit of time"). It's made complicated because English doesn't have a universally consistent pronunciation method. This is why through, though, bough, and enough are all pronounced differently (and likely why people are shifting to thru and tho; I haven't seen bao and enuf so much, though).
Anyway, the conversation started because the student hadn't used "an" in front of the acronym "N.F.R." (or something like that). So we went through the alphabet to collect the letters that use "an" (which are A, E, F, (H), I, L, M, N, O, R, S, X). The problem with H is that some people actually do pronounce it "haich" (most of them live in England), but I've heard people say, "a H" instead of the more commonly heard (at least in the US) "an H".
This brought us to the use of "a" and "an" with the word history. This word came into English with the Normans (I think), as historie; complete with the French habit of dropping the "h" sound completely. Since there was no "h" sound, then the word would have developed in the English language as "istorie", thereby requiring the use of "an history". However, I know many people who would look at "an history," "an historic," or "an historian" and say that it was wrong. Well, there's probably a reason for that: changing norms in writing, because English is a spoken language, and the "a" vs "an" debate is mostly about pronunciation.
Looking at Google n-gram viewer, you can see that the final shift away from "an historic"* occurred shortly after World War 2 (presumably with the rise of American publishing in comparison to British publishing). The shift away from "an historic" has only just recently been happening in British publishing.
I personally prefer using an historic over a historic, because of the existence of the word ahistoric. However, I think that I say (and write) a history, a historian, a histriography, etc.
* I chose to compare a historic and an historic, because a history and an history seems to have settled the change a LONG time ago, whereas the choice with historic is more recent. The n-gram for historian is even more dramatic than above.