Yes , they are . The confusion happens when people mix the two in common usage and when intended end usages collide . This is far more common than most would think .
Terminology is exactly that .
In the fence industry 2 1/2" pipe is a totally different thing from 2 1/2" pipe in plumbing . Same terminology , different application . Outside diameter versus inside diameter . This is only one of many examples .
Gaining clarity on these things is far more important than the argument over who is right and who is wrong .

Perfect. NOW I get it. Thanks for the explanation. This makes total sense to me.

Perhaps we should use the common term “vertical grain” that signifies the end grain orientation, rather than the term “quartersawn” that can be confused with how the log is sawn.

That would make more sense, but the entrenched traditional usage is here to stay I suspect.

Quarter sawn lumber refers to the angle at which the tree's growth rings intersect the face of the sawn board. Although there are differing opinions on the term, fully quarter sawn lumber is generally defined as growth rings that are 80 to 90 degrees to the face of the board.

Rift sawn lumber is usually used with oak to avoid the flecks that are common in the species. The annular rings or a rift sawn board are about 30-60 degrees to the face of the board, but 45 degrees is the most optimum

Pray for clarity ! Do it now ! The bottom line is that when you find yourself thinking that I make total sense you need professional help ASAP . ;)
Thanks .

So not to chime in late and confuse the conversation but also remember that the rings of most trees are not perfect circles. It is entirely possible to saw in the patterns above and end up with a rift sawn board where a quartersawn board should be (based on the cartoonish drawings)! I agree with the above that quartersawn from the sawmill standpoint is different than from the luthiers standpoint.

The way we did it when our family ran a sawmill was quarter the log, lay one of the now cut, fklat sides down flat and saw tha board. Then flip the whole quartered log and make the same cut on the other side. Then leaving the log in place make a second cut there, and again flip it to the other side--keep repeating. At the point where the rings were no longer perpendicular--we were now sawing rift--but it was not a different cut--the ring pattern had changed while sawing it the exact same way. Thery were not different cuts, just the center parts of the same quartered logs (center meaning after the perpendicular quartersawn boards were removed from the 2 sides of the same quartered log) depending on the ring pattern some of those rift could actually come out "quarter" and vice versa. It is the same cut on the same piece of wood but depending on the size of the log and the ring pattern, one may get dramatically different numbers of quartersawn and rift pieces. Next time you see a maple tree, notice they are frequently NOT actually very round. Those rings vary wildly after you cut the logs in quarters. Remember from a luthiers standpoint (today) many consider the quarter sawn pieces to be superior to the rift, but that is not true in all applications. Many feel the rift to be better wood for varying reasons (it will never cup and will stay straighter resisting warping). Many 58-60 Les pauls were made of rift--which can have excellent figure.
Also I will add my experience with Maple is nearly entirely with eastern hard (Sugar) maple and the softer Silver Maple. I have never sawn Western Bigleaf maple and never Mahogany or Rosewood. Only the trees native to the Nashville Tennessee area. But pretty much all of those! (Inlcuding but not limited to Walnut, Cherry, Persimon, and Osage Orange, and all the various pines and cedars (which are really juniper) that grow here.

I hope that all makes sense. Makes perfect sense to me in my mind but I also did it about 10 gazillion times so I am trying to describe that but it may not come through.

It makes perfect sense to a sawyers mind who has technical understanding of what types of cuts means what. For the luthier, as Charles mentioned earlier, all we care about is ||||||||||| Vertical grain. We don't really care how you sawyers manage to get that, or weather or not a log might have a wavey pattern in it as you cut it, as long as it comes out for us as |||||| Vertical we don't care ;)

Runout is another discussion but still...

:D, the main issue is the original op has asked what this all means showing a sawyers dissection of a log as it is different to how a luthier see's it, as mentioned in my post earlier, i use to work as a sawyer as a youngster on my neighbours sawmill, however I too also refer to the cuts as quarter, flat or off the quarter when talking with my customers and manufacturers

Now take a luthiers point of view on wood descirption and post that on a sawyers forum :)

It’s always difficult when the diagrams start with tree trunks that are perfect circles, and perfectly straight - those trees aren’t that common -