At the risk of confusing things further.....LOL (Honestly, I'm trying my best not to.)
An image taken by a digital camera has a resolution determined by the camera sensor's setting for example at a setting of 6MP the image will contain 6 million dots of detail.
Well this is where the confusion comes into play:
Tom Mann has quite correctly said that the more 'common' understanding of the word 'resolution' defines how many pixels are in the image...as you've demonstrated in your above statement.
Now, I agree wholeheartedly with that, but there is another meaning of the word 'resolution' which is the one
I stand by and believe to be the [less misleading?] definition, namely that 'resolution' is a ratio of the amount of pixels per a linear measurement, hence the term 'Pixels Per Inch'...the amount of pixels is irrelevant.
Both a 1x1 px image and a 1000x1000 px image could have a 300ppi or a 1200ppi resolution written to their meta-data....or even 1ppi.
6MP is just the total number of pixels, from just this info you cannot even determine the dimensions of an image....it could be 1px high by 6Mpx wide....who knows? This is why, along with other information, that the real dimensions are 'written' into the meta-data, it is not calculated. 'Resolution' is another piece of written info, it bears no direct relationship to the image itself...it could be anything.
(Just to add, the actual dimensions of a digital image are determined by the image data but any software that shows you the 'image dimensions' will use the info written in the meta-data.....and yes, you can write anything for this too...3 x 2 pigs or 3072 x 2048 plum puddings, for instance).
There are many applications capable of writing this information, Photoshop is just one of them. When you 'set' the resolution in PS all you are doing is writing that information to the meta-data, it has no effect on the image. (See later about upsampling and downsampling).
*
My argument, (And I really hate to call it that), is that a DIGITAL image cannot have linear measurement, you cannot get a ruler and physically measure how big a digital image is....its just a grid of squares. Based on that, without a linear measurement a DIGITAL image cannot have a 'resolution', (you need both pixels and length), but it can inherit the 'resolution' of the medium on which it is being viewed.....99% of the time this will probably be an LCD screen of some sort.
Every LCD screen does have a 'resolution', you CAN physically measure it. Therefore, any image you view on it 'inherits' that 'resolution'.
Although an image file might contain 6 million dots of detail, the number of dots actually displayed will depend on the screen which is displaying the image. A High Definition screen is only 1920 x 1080 = 2073600 ie about 2 millions pixels so can only display about one third of 6 millions pixels.
@100% zoom, yes.
Obviously if you want to view all the image you have to zoom out, in your example that would be to around 33%.
I would say that to view an image at its best you would ideally need 1px of your screen to denote 1px of the image....sound logical?
You would, therefore, assume that 100% zoom would give you that 1px per 1px relationship, but, as I said before, Windows OS has a default 'dpi' setting of 96dpi which is probably not the same resolution as your screen.
One way you can, and I stress,
can, overcome this is by changing the default dpi in Windows to match that of your screen, but as most software is written for the default 96dpi many will 'break' if you change it.....so you're pretty much stuck with it....so...
...Photoshop has a handy 'Screen Resolution' setting under Preferences > Units and Rulers.
Here you can set your actual screen 'Resolution' to give you a more accurate 'Actual Size' image on your screen.
As a test you can try this

With PS Screen Resolution @ 96dpi)
Check the 'resolution' of your OS. For windows 7, right click the desktop, select Personalize > Display > Set Custom Text Size (DPI).
In the resulting window the 'dpi' for the OS should be displayed, 100% = 96 pixels per inch.(Unless you've already changed it)
Cancel out of this.
Measure the Width of the visible area of your screen, pref in inches. Divide your screen width in pixels by your screen width in inches....this will give you an approximate PPI for your screen.
In photoshop create two rectangles, one 960px wide (OS dpi x 10) and one (<your screen PPI> x 10)
View at 100%....('Actual pixels' for pre CC) and position so you can see the first rectangle.
Mark off 10 inches on a piece of paper, hold that up to the rectangle to compare widths......no where near 10" right?
Now check the other rectangle.....a lot nearer, yes?
This shows that its the OUTPUT device (in this case, your screen) that denotes the resolution of an image and changing the 'resolution' of that image via software does not have an effect on how you view it.
So if you want to view images on your screen at the same size as when printed out, change your Screen Resolution in PS and use View > Print Size.
For this to work you would then need to change the 'resolution' of the image to whatever your screen resolution is. (Yes I know I said it had no effect but 'Print Size' is determined by the dpi and pixel dims....so despite it being displayed on-screen it needs to be treated as if it was going to a printer).
I don't have a mac but I assume it's default dpi is 72, and retina is 144.....this is based on a screen shot posted here from someone with a retina display mac....its resolution was written as 144dpi.
Were you to use a PRINTER as the output device then you would have to tell the printer the relationship between the amount of pixels in the image and how much of the paper those pixels cover. A printer does not have its own 'grid' of pixels like a screen, so you need to supply it with that info. Just supplying the amount of pixels or the pixel dimensions is not enough information for the printer to determine how big to print the image....hence it needs that relationship....or ratio...or DPI.
As I said before, if you are NOT sending the image to a printer, or to be printed elsewhere and you don't want to view using 'Print Size' , you can ignore the dpi of an image.
*If you intend to upsampling or downsampling an image though then dpi does have an effect but as this is generally regarded as bad practice I'll not go into it.
I dunno if that's going to clear things up, and like I said this is just
MY interpretation of how things work, you can make up your own mind as to whether you agree or not.
Regards.
MrTom.