Let's clear something up right away:
Most of these adjectives were created as marketing terms, so they DO NOT have a standardized way of defining them or even ensuring that the label is accurate between the brands. The brands are allowed to determine this by themselves. Most of the more reputable brands are very good at adhering to their own processing standards, but in all cases, it is important to realize that there is no one agreed upon definition for these things, nor is there an independent body who verifies that these claims are, in fact, true. This accounts for almost all of the discrepancies between one brand's definition of these terms and another.
So what does "virgin" mean?
In spite of pie-in-the-sky claims you may hear on eBay or at your local BSS, virgin only reliably means one thing: the hair hasn't been color treated or permed. THAT'S IT.
Here's the scoop: ALL human hair - even "virgin" human hair - has to be processed.
That shouldn't be too much of a revelation, actually, since that hair is no longer attached to the person who grew it.
Cutting it off the person who grew it = processing
Treating it for hygiene concerns (such as de-lousing it, because remember that much of it is coming from poor countries) = processing
Sewing it into wefts to be added to a wig = processing
Sewing each individual strand into a hand-tied cap = processing
Cutting and styling that hair once it's on a wig = yep, this is still technically a form of processing!
How is virgin human hair different from Remy (Remi) hair?
Most Remy hair is color treated, for starters. There's more to it, though. Remy hair is hair where all of the cuticles are present in some capacity and run in the same direction from root to tip to prevent tangling. Remy hair can be virgin, and virgin hair can also be Remy. Just because you see one of those terms present, though, does not automatically imply that both are true. They are NOT synonymous, but they also aren't mutually exclusive.