The Architectural Woodworkers Institute defines "rift sawing" as a technique of cutting boards from logs radially so the annular growth ring orientation is between 30 - 60 degrees to the face of the board, with 45 degrees being "optimum".
https://www.youtube.com/watch?v=VvUPJPFg4wM
AWI defines quartersawn lumber as having annual growth ring orientation between 60 - 90 degrees relative to the face of the board.
Flat-sawing produces the least wood waste and fastest sawing, but produces boards which are more susceptible to cupping and shrinkage, and which have a distinctive grain which may be aesthetically undesirable for some uses. Quarter sawing produces smaller boards than flat sawing, but has a straighter grain, which in addition to being visually pleasing, makes the lumber more stable.
This rift grain lumber is also referred to as "bastard grain" from Hoadley.
Hoadley also tries denote rift grain and quarter grain as interchangeable definitions, but they are not according to the AWS, so confusion of the terminology is understandable.
If someone from the architectural woodworking institute is reading this, please replace the picture listed with the one you have on page 449 in appendix B of the 2009 1st edition of Architectural Woodwork Standards. It gives a much clearer picture.