Does the former have a typo or are they synonyms? Do they always have the same meaning? Please enlighten me as I am confused on this matter.
The word was originally minuscule, borrowed from French. The minuscule spelling has always been the preferred spelling. However, miniscule is not as simple as a typo. According to the OED, the first citation of the miniscule variant is from 1871, so this is a form that has been around quite a long time.
The OED says the following about miniscule:
Variant of MINUSCULE adj., probably arising partly from shift of stress from the second to the first syllable, and partly from association with MINIATURE adj., MINIMUM adj., etc.
So, there are two reasons that miniscule persists as a variant.
The first is the shift in stress. In English, unstressed vowels are often reduced to schwa, [ə], no matter what the fully stressed vowel would have been. Minuscule used to always be pronounced with stress on the second syllable (containing the "u"), and was therefore unambiguously an [u] sound. When minuscule began to get stress on the first syllable, it was no longer clear from hearing the word what the second vowel was.
The second was the existence of semantically similar words that contained the spelling mini, such as miniature and minimum. The word mini is associated with small things.
Therefore, a person spelling the word minuscule, having no auditory cues to indicate the spelling "minu", and knowing other smallness words contain "mini", has every logical reason to think the spelling should be "miniscule".
I fully agree with the foregoing responses to the spelling of minuscule. As a former Latin student with English minor, I think the time has arrived to welcome "miniscule" as a full fledged member of that amazing, non-holds barred, ever evolving English language, and, as such, give it the meaning it deserves rather than demeaning it superciliously to the level of an accepted misspelling of minuscule. As "the sunneversets, Hooper and Robusto" point out, "minuscule" is the opposite of "majuscule", two vocables which are logical and elegant in French but for which the English language, in dogged resistance to yielding to Gallic influence, resorts to lame phrases such as "upper case" and "lower case," borrowed from printers' vocabularies and preferred as evidence of technical savvy used by the literati of spelling. Let "minuscule" and "majuscule" be returned to their comparative significances of size and elevate "miniscule" to membership in the language, on a par with its step-homophonic relatives, such as miniature and minimum.
Minuscule is the generally accepted and earliest form. Miniscule appeared later, and is regarded by some as an error, and others as a variant. If you use minuscule, no-one will be bothered, but if you write miniscule, some people will think it is a mistake.
See these references for more...
I would imagine "miniscule" became prevalent because everyone made a false association between it the more common word "miniature". When in fact it's more like "minus". (A similar word that everyone gets wrong by coming to a false conclusion about its derivation is "supercede" instead of the actual correct word "supersede".)
As Brian Hooper says, some people will think you've made a mistake if you spell it "miniscule", but miniscule is now listed as a legitimate variant in dictionaries, simply because spelling it this way is now so common. As an ex-Latin-student it really annoys me to see this spelling, but what can you do?