How can two pictures of the same size still appear to be a different size? (Photoshop CS6 problem)

Question

I called the big webdesign file "(X)" and the image I wanted to paste in it "(Y)",
so that you won't be confused when you read it.
What Happened
For the design of a webpage, I made a photoshop-file(X) with a lot of squares(X). These squares(X) had the size 9,42×9,42 centimeters.
I measured the squares(X) carefully and also made sure the size was in centimeters, so I am sure that the size was 9,42×9,42 cm.
My plan was to fill the squares(X) with pictures(Y). I had a map on my computer with a lot of square-sized JPG-images(Y) in it. All I had
to do was open the pictures(Y) in photoshop, change the size into 9,42×9,42 centimeters and copy+paste them into the squares(X)
of the webdesign. I did this before and it worked perfectly.
But then, I opened one of the images(Y) and when I wanted to resize it, the resize-tool said it was only 3,25×3,25 centimeters big.
I thought it was strange, so I copied+pasted it into the design-file(X) with all the squares(X) that needed to be filled. Allthough photoshop
had told me that the squares(X) in the file were 9,42×9,42 centimeters big and the image(Y) I resized was 3,25×3,25, the "small" image(Y)
turned out to be bigger then the squares(X). And when I resized the "small" image(Y) into 9,42×9,42 centimeters, it was even bigger
than it was before. How can this be, and how can I still make the images(X&Y) the same size?
What I already tried
- I made the file of the webdesign(X) with all the squares(X) into one layer, copied the file(X) and opened a new file(X) with the same
measurements of the old file(X). I also changed the resolution of the file(X) into pixels/centimeters instead of pixels/inches.
Then I pasted the image(X) of the old file into the new file. I didn't work; the image(X) that I pasted in the new file was bigger and
when I pasted the other picture(Y) in this image, the same problem was still there.
- I also opened the picture(Y) in photoshop, made a screenshot of it and then pasted the screenshot into paint. With paint I cropped
it again and saved it as a JPEG-file. After that, I opened the image (Y) in photoshop again. It now had the size of 11,27×11,27 centimeters.
Then I resized the image(Y) into 9,42×9,42 cm, but it still wasn't as big as the squares(X).
Could you help me please?
I really don't understand why this problem is happening and I can't think of a solution because I am still quite unexperienced with photoshop
and I also couldn't find the answer on the internet. I assume the solution is very simple, but I haven't found it yet allthough I have to finish this
project soon and I also have to use the image(Y). So any help would be very appreciated.
Thanks,
Simone

Answer 1

You need to understand the basic of a digital image.
Image is recorded as pixels and image is a rectangle so many pixels wide and so many pixel high.   Pixels do not have a fixed size. The images resolution setting defines the image current pixel size.
So for example if you have and image that is 300 pixel wide and 200 pixels high and set its dip resolution to 100DPI the image size is 3" wide and 2" high.  Set its dip setting tp 300DPI the image size becomes 1" wide by 2/3" high.  Both the 3" x 2" and the 1"x2/3" images have the same 60000 RGB Colored Pixels.
Web pages are sized to to be so many pixel wide and so many pixel high.  Often the height is not enforced scrolling is used when viewing. 
However image for web pages often must not exceed so many pixel wide and high for displays have a fixed resolution and a fixed number of Pixels. You want images to fit on users displays.  Users use different displays some have high resolution displays and other have low resolution displays with far fewer pixels then high resolution displays.
Web Image are normally image that have been interpolated down in number of pixels a resampled large image so that web image will fit on a low resolution  display with limited number of pixels. The image size the user see depend on the display they are currently using. A low resolution display's image will be much larger then the same image displayed on a nexus 10 with a 300dip display. Cheep low cost Desktop LCD have a 84DIP resolution, large high cost desktop displays are not be much higher in resolution somewhere near 108DPI.   Tablets, Laptop and Phones can have much higher resolution like the nexus 10 300DPI IPS display