I'm no authority on the origin of these terms, so if you have information on this, share it with us.
I can answer some of the questions; I invite corrections on the history though.
The Golden Ratio gives a rectangle such that if you add a square on the long side, the new rectangle is the same shape. This leads somehow to the biological/mathematical fact that spiralling growth tends to settle on this shape.
The history I have heard of the 3:4 and 2:3 ratios, plus wider ratios for moving pictures, is this:
a) Early movies settled on the 35mm format of Edison and Eastman, with a 3:4 shape (24mm across the film, 18mm along it).
TV copied this shape for obvious reasons; computer monitors copied TV's, early digital cameras used sensors originally designed for TV; hence the persistence of 3:4.
c) The 35mm movie frame was deemed too small for the higher quality standards of a stationary image, and Leica decided on the solution of "double frame": two movie frames became one 35mm still frame of 24mmx36mm. (Thus the so-called "half-frame" was the original, sometimes called "single frame" in older photography books.)
d) The movie industry reacted to TV by differentiating themselves with wider formats often just by cropping the frame to less than 18mm high). TV is only now responding with HDTV.
e) For many decades, almost every 35mm film print was cropped to a squarer shape; even standard prints used to be something like 3 1/2" by 5" (a ratio about 1.43) up until about the 1970's; probably originally a convenience based on halfing a 5"x7" sheet. (Why not quarter an 8"x10" sheet to get 4"x5" prints? I suspect that shape was considered a bit too square for snapshots, with too much sky and foreground in the average landscape.)
f) In the early, contact printing days of photography, various film sizes were somewhat commonly used, and the main ones I know of are 8 by 10, 5 by 7, 6 1/2 by 8 1/2, and 6 1/4 by 8 1/4. All are squarer than 2:3, and the last two get very close to 3:4.
g) The one new photographic frame shape adopted "from scratch" in recent times and widely accepted by serious photogaphers is 645 medium format; actually most brands are 41.5mm by 56mm, or almost exactly 3:4. Strangely, it is often said wrongly that its shape exactly fits 8x10 prints; in fact it is close but a bit "longer".
Given all the historical contraints in photographic equipment and printing supplies, I looked at painting and drawing supplies where shapes are far more flexible and there are many more choices of size and shape used; this lead to my observation that 4:5 and 3:4 are the mainstream favorites, with a huge array of other options appropriate for various situations of course.
Finally, the new 4/3" format is only a new size, preserving the predominant digital frame shape of 4:3 while about doubling the 2/3" format that is currently the upper limit in compact digital cameras; and with a cute double meaning in the name.