Dark Data refers to actual data in the narrow sense (bits and bytes, text, images, sound and so on) with certain characteristics, mostly around being neglected or underappreciated in some way.
The following statement therefore makes sense:
We've accumulated 100TB of dark data that we have no idea what to do with.
Big Data is a set of technologies, practices and solutions related to solving business problems in a particular way, mostly a variation on collecting and storing vast bodies of information and using it to some purpose. Big Data does not typically refer to data in the narrow sense (bits and bytes, etc.).
Consider this:
We've accumulated 100TB of big data on our servers.
Doesn't it sound awkward?
As you may tell, Big Data is more of a marketing/business metaphor. When Marketing picks up the scent of Dark Data and turns it into a buzzword like Big Data, then we can start comparing them apples to apples. But for now, we have:
Dark Data == underutilized and underappreciated data
Big Data == collecting, storing and analyzing vast bodies of information
With that in mind I can attempt to divine the meaning of the initial quote stating that "up to 90 percent of big data is dark data" (wording which I personally find lame and mostly designed to grab attention):
Up to 90% of data collected under Big Data initiatives is not utilized to its fullest potential: most of its real value still lies hidden and unrealized.
I'm guessing the rest of the piece talked about how data science is still in its infancy and how much work still lies ahead, if we ever hope to tap all those unseen insights.