Confusion has often existed on these forums concerning the distinction between the various types of tournaments (and rules) vs the various types of ratings.
There are three types of USCF-ratable tournaments:
- Regular (scorekeeping required)
- Quick (scorekeeping optional)
- Blitz (all sorts of weird rules, like capturing the king)
Each has its own requirements for time controls.
And there are two rating systems:
- Regular (for slower time controls)
- Quick (for faster time controls)
The following diagrams illustrate which rating systems are used for which tournament types. Black pieces represent the tournament types:
Regular = R = rook
Quick = Q = queen
Blitz = B = bishop
White pieces represent the rating systems:
Regular = R = rook
Quick = Q = queen
As the first diagram shows, the regular rating system (white rook) can rate (capture) regular tournaments (black rooks), while the quick rating system (white queen) can rate (capture) quick tournaments (black queens), blitz tournaments (black bishops), and some, but not all, regular tournaments (black rooks):
If, however, USCF were to develop a separate blitz rating system, the diagram would change somewhat:
The quick rating system would no longer rate Blitz tournaments. Instead, the new blitz rating system would take care of that.
However, it is entirely possible that the ratings committee might decide that, just as quick ratings can also rate some regular tournaments, the new blitz ratings could also rate some quick tournaments (say, those with time controls faster than G/15). In that case, the diagram would now look like this:
I hope this clears up all the confusion. 
Or maybe the confusion will increase, resulting in a lively debate.
Please note, in particular, that there is no such thing as a “dual” tournament type, nor a “dual” rating system. A dual-rated tournament is nothing more than a regular tournament that is also rated by the quick rating system.
That explains, for example, why I often say that G/25 d/5 (beginning 1-1-2012) is regular while G/25 d/3 is quick, and I don’t use the word “dual”.
Bill Smythe