You are some confused people. Also: Totally wrong. I dont blame you, its complicated. I will try to explain, hopefully I can help you.
Ok, lets start with the default. The 15" screen used to have 1440 horizontal and 900 vertical pixels. UI elements all had a certain pixel size that made them a certain size on the screen. The menu bar was 20 pixels high, for example.
Now, the screen has 2880 horizontal and 1800 vertical pixels, exactly double in every dimension. If you were to use the old UI elements they would only look one quarter their size. The 20 pixel high menu bar would still be 20 pixels high, but it would look half as high on screen.
Apple didnt want that, Apple wanted everything to remain the same size. They consequently pixel double everything (pixel quadruple if we are talking about two dimensions). So the menu bar was increased in size by Apple, from 20 to 40 pixels high. That 40 pixel menu bar still looks to have the same height as the 20 pixel bar on a 1440×900 screen. They also created new versions of all the artwork, e.g. the Apple in menu bar was recreated with four times as many pixels. That, again, makes it the same size on screen.
This approach, however, is limiting for Macs. On iOS it makes perfect sense: apps are baked to be a certain size, they arent even set up for changes in size. On OS X, however, all apps are resizable. There is really no need to always have UI elements and content be the same size. You can make it smaller. Making UI elements and text smaller on iOS devices would just get you black bars around the edges of the screen, on OS X it actually gives you more space to work with.
How can you take advantage of that space? First, we probably have to think about why Apple picked the pixel doubling (or quadrupling) strategy. The great think about pixel doubling is that every four pixels on a Retina screen map to one pixel on the non-Retina screen. That way, you never end up with fractions of pixels when displaying non-Retina apps on a Retina screen. x number of pixels on the non-Retina screen always equal 2x number on pixels on a Retina screen, that is always an integer. If the multiplier would have decimals, you would end up with fractions of pixels. When your screen tries to display fractions of pixels they will look blurry.
Another advantage of Apples approach is convenience. Developers just have to create versions of all their artwork that is four times as large as their originals. Thats easy to remember, easy to do.
Ok, now back to taking advantage of that space. First we will think about what Apple does in terms of a non-Retina display. Say you have your nice non-Retina 1440×900 screen but you are jealous of your friend and her nice 1650×1080 screen. You want to be able to display as much stuff on your screen as she can but you dont want to get a new screen.
What you could do is just render a 1650×1080 and then resize that rendered image to 1440×900. If you ever had a VNC session with a computer with a 1650×1080 screen from a computer with a 1440×900 screen you know how that looks. The problem with that approach is that it is ugly. The pixels on a non-Retina screen are too large, you end up with fractions of pixels (when resizing the rendered 1650×1080 to 1440×900), thats just not nice or elegant.
But exactly that approach is practical now, with Retina screens. They have so many pixels that you can get away with fractions of pixels. Apple is still no comfortable with that, thats why pixel doubling (with no fractions of pixels) is the default, but they give it to you as an option. It basically works the same.
Its best to just ignore the old pixel resolutions at this point. They are not helpful and they dont figure into it. They play no role, they are just there to tell you what you can expect in terms of an old display, in terms of numbers you might be familiar with. In practice (and as is evident here), however, they confuse.
Ok, so you got your 2880×1800 screen. Apple created artwork for everything that is four times as large and thus has the same size as the old, smaller, artwork on a non-Retina screen, it just takes advantage of all the pixels.
When you pick an option that gives you more space (say the option that confusingly says Looks like 1650×1080), Apple takes that exact artwork, but renders it at 3300×2100. If you had a hypothetical screen with a resolution of 3300×2100 everything would look crisp and every four pixels would map to exactly one pixel on a 1650×1080 screen. More interestingly, however, UI elements on this hypothetical Retina-screen would have the same size as UI elements on a 1650×1080 non-Retina screen with the same size.
Apple basically renders to a virtual 3300×2100 Retina screen, using all the Retina artwork. Were they to start selling a screen with that resolution tomorrow, OS X could just take that render and throw it on such a screen, it would look perfect.
Problem is: The 2880×1800 screen just cannot display 3300×2100 pixels. So, OS X just resizes those 3300×2100 pixels down to 2880×2100 pixels. Thats not perfect (because in the conversion process you do end up with fractions of pixels), but since the pixels are so small on a Retina screen, the added blurriness from fractions of pixels is hardly noticeably.
Did you see? When OS X says Looks like 1650×1080 they actually mean it. You Retina display still uses every single pixel. The screen resolution is not changed to 1650×1080, it remains firmly at 2880×1800.
I hope that helps you understand how this all works.
