In his Complete Guide to Perspective Drawing (page 39), Craig Attebery places Measuring Points of two-point perspective in a line perperdicular to that crossing the Station Point and the Center of Vision:
LVP, RVP = Left/Right Vanishing Points
LMP, LVP = Left/Right Measuring Points
SP = Station Point
Later, on page 179, the author uses a different method for three-point perspective, in which the Measuring Point line does not cross the Center of Vision/Station Point line at a 90° angle. I would like to know why.
LVP, RVP, VVP = Left/Right/Vertical Vanishing Points
LMP, LVP, VVP = Left/Right/Vertical Measuring Points
LSP = Left Station Point
Note: Notation in red was added by me
The method is the same. In one- and two-point perspective, the vertical vanishing point is at infinity, which effectively means that the left reference line (i.e., the line through LVP and CV) coincides with the horizon.
In other words, when you say that Attebery "places Measuring Points of two-point perspective in a line perpendicular to that crossing the Station Point and the Center of Vision", this is true, but it's a coincidence. (Note that it's also not the way he describes it.)
When learning perspective, we start with one-point, and work up to three-point perspective, since it's much easier to gradually introduce concepts this way. One- and two-point perspective are convenient because a lot of things line up nicely—but it's this very convenience that can lead to confusion.