Coming at this from the viewpoint of a woodworker, this debate has turned into apples and oranges. Keith's examples above are correct, but from the perspective a sawmill. When you go to the lumberyard, it all changes somewhat.

Wood is sorted/graded according to figure, and whether it is considered flat, rift or quarter sawn is based on the orientation of growth rings in the board.

In the above example, all the boards from the riftsawn log will be sold as quartersawn wood, the growth rings are uniformly perpendicular to the board.
The boards from the quartersawn log will be mixed quarter and rift, the riftsawn boards being those with growth rings closer to 45 degrees.
The boards cut from the plainsawn log will be sold as flat, rift and quartersawn. The boards from the center will be marked quarter, the boards from the outside edges will be marked flat sawn, and the boards from in between will be marked riftsawn. The grain examples under the plainsawn log aren't exactly correct because they only show examples of flatsawn boards, that should also include the examples shown under the quartersawn log.

Like I said, that is how the lumberyard sells wood, how the log is sawn means nothing to them, they are only concerned with the grain of the wood. Some wood is sorted by figure/growth ring orientation and some is just all thrown into a pile.

If you look this up on the internet, you're likely to just get confused. If you go to a good lumberyard, and find an employee who knows his business and ask him the difference between the different boards in the white oak stack, he'll tell you the difference is based on the growth ring orientation in the board and how it affects the look of the board, and unless they saw their own logs, he won't know what method was used to saw it.

Tim