Hi Tom -
It would be a lot simpler if the word, "resolution", was only used in the sense you described in your post (which seems to be more or less the same as my definition #2 in the 1st post in this thread), ie, essentially, how large (in units of inches or cm) each pixel in an image is. This definition tends to be more commonly used to describe the output end of things (eg, prints and images on monitors), but can equally well be used to describe input devices (eg, "a CCD sensor with 1000 pixels per cm").
Unfortunately, by far, the more common usage of the term, "resolution", is that it is the number of different "things" that one can see in an image (ie, my definition #1). This is effectively the total number of pixels in an image (ie, megapixels) or the pixel dimensions of the image. This is the common meaning of the term by laymen, as well as definition used by camera manufacturers when they characterize their latest and greatest product as being a high resolution, 99 zillion megapixel DSLR, LOL. This information content definition is also the what is meant when you read in the newspaper that a spy satellite or the Hubble telescope is "ultra high resolution".
There is no getting around the fact that there are two different, equally common uses of the term, and if one tries to convince yourself or others that they should ignore one or the other definition, you'll be fighting a battle that you can't win. IMHO, the best approach is to use the context to determine which definition is being used at any particular moment, realizing, of course that the writer may not even be aware of the other use of the term.
I try to avoid such confusion in my own writing by referring to one as "dpi" or "ppi", and the other by "pixel dimensions", especially, the first time I use the term resolution in an article, in class, or in a web post.
Tom M
PS - re your statement, "...A printer will read this information and use it to calculate the image size when printing...", for the vast majority of prints made in the world (eg, by printing kiosks in stores, when ordering prints at a camera store or on-line at places like Mpix or Snapfish), your statement simply is not true. Rather, the customer submits a file with some pixel dimensions (probably unknown to them), and specifies the size (in inches) of the print that they want. The vendor's software then calculates the resulting ppi, and if it is too low, automatically up-rez'es your image so that the customer don't see individual pixels, just a bit of a blur. The customer/user never has to deal with concepts like ppi, and if some ppi metadata happens to be stored in your file, it is simply ignored.
In fact, in many cases, even if you are sending your file to a local printer directly attached to your computer, the same also holds. The driver software for many consumer grade printers simply asks you to fill in what size print you want, and it does the rest. This is in contrast to more professional grade programs (like PS) and pro or semi-pro printers that work the other way around and make use of the ppi metadata as you suggested in your post.
