Scale
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Traditional cartographic scales have very little meaning in computer graphics. Explaining this has been a perennial problem for me, especially since mapping software just glosses over it for the most part by providing some kind of "good enough" translation of e.g. 1:1000 to something on screen.

Unless you calibrate the software to the exact size of the display in real-world inches, there's no way to know exactly how big in inches a 100' object on the map will appear to be. 

The problem is exaggerated for projector displays, since the size of the actual screen depends entirely on arrangement and the computer has no idea how big things are.

So, we use feet/pixels, because pixels are knowable even though the actual size of the pixels is not.

Paper is a simpler situation - sort of. Realistically we're still passing around digital data - PDFs or images or whatever - and it's up to the user, software, operating system, driver, and printer to determine what the actual scale is when it's rendered to paper. For example, take the case of a PDF legal-size document that is printed on letter-size paper with scaling enabled.

The PDF software packages we use have a convention that a pixel (since we're still drawing using computer graphics terms, even if to pdf) is equivalent to a typographic point:

en.wikipedia.org/wiki/Point_(typography)

So, each pixel is 1/72 of an inch on the virtual page and therefore intended to be printed as such.

However, we found that this convention resulted in printed results that were much larger (in real world) than what you see on the screen. So we actually scale everything again by a factor of two, such that 1 inch on a virtual page is 144 pixels as drawn. Modern displays are becoming even higher resolution; retina displays are 250-350 ppi. Laser printers can be 300-1200 dpi. But, once again, it's a matter of perception - whether the paper looks close enough to that seen on the screen. 

Thus, if you're plotting a snapshot taken at a scale of 10 feet/pixel, each virtual paper inch will be 1440 feet. Assuming you print it at the same scale as the PDF specifies, and there's no monkey business with the margins, then that's the actual scale - you can convert it to a ratio by multiplying by 12, so 1:17280.