As for the systems themselves, based upon what I've read, I've come to the tentative supposition that their data storage, categorization, and compartmentalization is relatively minimal and undifferentiated. [1]
This would be in line with what we learned about the structure (or rather, lack thereof) of intelligence systems of the State Department and military that allowed Manning to acquire such a broad range of documents undetected.
What I've seen cited of the documents from "agency who shall not be named" appear to describe and show that definitions of and limits upon what is searched for, are largely manually constructed and executed by the human operators performing those searches. "You may search for this OR that, but not both. You may search for this other but only in conjunction (AND) with this other term.
It all reminds me rather of one job I had that involved extensive data mining. I started with a mass of raw detail records and winnowed things down. It was entirely up to me what ended up being winnowed out, and I required both extensive knowledge of the domain and careful and precise execution in order to come up with the correct results.
The whole "unnamed agency" situation has developed rather a similar smell, for me.
As an aside, today when I read about the Manning sentencing, one of my first thoughts was, "Supposing that this prosecution has been 'fair' and 'necessary' (not that I necessarily agree with this supposition), then where is the prosecution and sentencing of those responsible for the criminally negligent design and management of the data intelligence systems he 'exploited'?"
For all its vaunted capabilities, I suspect that data management at the NSA is similarly fucked up, and that there are managers and contractors who should and would, in a fair world, be sent to prison for this.
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[1] Perhaps with a few exceptions, e.g. for senior government officials and favored members of the private "elite" class, e.g. the C suite and board of Goldman and the like.