I think you have this a bit backward:
1) asides – “twitter” style messages
2) status – “facebook” style messages
Think of status as a Tweet or Facebook status update: a text-only or text-and-link-only post of around 150 characters or less (140 seems to be a good number, thanks to Twitter).
Think of an aside as a brief post, of one or two paragraphs, usually without a Title.
The problem with the term aside is that its use (and nomenclature) is not dictated in any way whatsoever by the historical use of the term “aside” in literature, drama, etc.
Instead, the use of the term comes from Matt Mullenweg’s personal site. Matt started writing brief, un-titled Posts, which he categorized as “asides”. One version of his personal site’s Theme (Mazeld, perhaps?) started creating a custom loop for the “asides” and “gallery” categories.
These custom loops became the origination for the concept of Post Formats, and unfortunately, the term “aside” was retained as one of the Post Format types.