The term for pixels per inch of image resolution has always been called dpi (dots per inch). This may be pre-press jargon, but it has always been the proper name. The concept of a pixel is in fact sort of a colored dot (see more). This usage has always been that dpi means pixels per inch of image resolution when printed. We also hear the name ppi for pixels for inch. Same meaning, and interchangeable, both are acceptable, either can be used.
The problem is that printers also use the term dpi a different way, about the spacing of their own ink dots per per inch - for example the spacing of the CMYK ink drops that ink jet printers can print. Ink drops are NOT pixels, and these are very different concepts. Image pixels might be one of 16.7 million colors (24 bit RGB color). But the printer may only have four colors of ink (CMYK), so that every ink dot is only either Cyan, Magenta, Yellow, or Black ink. The printer has no other choices. It can only make ink drops of four colors to simulate printing our pixels. The only way to simulate 16.7 million colors with four colors of ink is to "dither" it, printing a group of several ink dots as needed for each pixel, combining the four colors of ink dots within that pixel area, to average out and simulate printing one of the 16.7 million possible colors for one pixel (See more).
So to print 300 dpi image pixels (one definition), the printer needs to use perhaps 2400 dpi of ink dots (the other definition), to be able to simulate the pixel colors (called dithering). Both use dpi, both are correct, both do mean dots per inch, but the first "dots" are pixels in the image, and the second "dots" are ink drops from the print head, which is a very different concept. The printer dpi setting is a quality setting. The higher the printer dpi setting, the more ink dots are available in the pixel space to simulate the color of the one image pixel. This higher ink dot setting is called Photo Quality mode. The lower the printer dpi setting, the faster it prints, but the more crude the image appears, and this is called Draft mode. We print the same image at 300 dpi either way, but our ability to reproduce the pixel color has greatly changed.
So... there are two uses for the term dpi, as described above. This does confuse newbies, until they grasp the concept. Then it becomes very clear once we understand the only way it can be. The context where it is used tells us what it has to mean. It can only mean one thing. If the "dpi" context is about an image, dpi means pixels per inch when printed. There can be only one interpretation, as there are no ink drops in any image file. If the "dpi" context is about the printers quality setting, dpi is about ink drops per inch. Printers print ink drops. Like all English words, the context of the way it is used can only have one meaning.
And now, ink jet printers are changing too, and many no longer specify these quality settings as 300 dpi for low quality, or 2400 dpi for high quality. Instead most simply specify Low Quality or High Quality mode now, which is what it means, and is all we need to know. This should help.
Image resolution has always been called dpi, it is simply the term meaning pixels per inch. But the term ppi for pixels per inch is very descriptive too, and is perfectly acceptable. Both terms are correct. And we need to know this, because we will see it both ways all the time.
Written as an argument, specifically for those vocal newbies that want to argue their nonsense notion that the only acceptable name for image resolution is ppi.
If you use TIF, JPG, or EXIF data, your images are using dpi, like it or not. The file specifications are written as "dpi", meaning pixels per inch. There are no ink drops in image files.
The JPG image file format specification stores image resolution in "dots per inch" (page 2 and page 5)".
The EXIF 2.2 specification says dpi everywhere (search for dpi, about 20 references).
The TIF file format specification stores image resolution in "dots per inch" or "dots per cm" (Resolution Units, page 38).
So exactly who are you to call these authors of the most common file format specifications wrong?
All scanner ratings are specified as dpi, obviously meaning pixels per inch. They don't say "samples per inch", they all say dpi, which we all know means pixels per inch. Scanners create pixels, not ink dots. Who are you to call every scanner manufacturer wrong?
All continuous tone printers (dye subs, Fuji Frontier class, etc) print pixels, and call their ratings dpi too (colored dots also called pixels). Who are you to call all these manufacturers wrong?
When calling everyone else wrong, a wise man would reevaluate his own position. Claiming dpi is misuse is obviously dead wrong, and is only wishful thinking that the world OUGHT to be as you wish it to be. On planet Earth, the two terms dpi and ppi are obviously interchangeable regarding image resolution. Wake up, look around, where have you been? Pixels per inch has ALWAYS been dpi. Yes, dpi does also have another use. So what? Almost every English word has multiple meanings and uses. Both terms are obviously used (dpi = pixels per inch, and dpi = ink drops per inch) and that matter is long settled. As for dpi and ppi, say it yourself whichever way you prefer to say it, but we obviously must understand it both ways. Because we obviously see it everywhere both ways.
In fairness, BMP and PNG file specifications specify resolution as pixels per meter. My point is NOT that dpi is the only correct term. My point is that both are used, and dpi is NOT wrong.
This whole notion of sematics about dpi is really dumb. For example, my big dictionary has 116 definitions for the word "set". First one is to put something in a particular place, and the last one is stubborn or obstinate.
The analogy is that some of us are obstinate, insisting words can only have one meaning, specifically insisting the only possible valid definition is the one they are able to understand. Sometimes when newbies figure out there are two definitions, some of them go crazy inventing their own rules for the rest us to abide by. Specifically some want to now reserve dpi for printers, and to only use ppi for images. It might have been defined that way, but it was not defined that way, not in any real world.
The point important to me is that since dpi and ppi are obviously used interchangeably, this interchangeability should be explained to be helpful to novices, so they can understand what they find to read in the real world. It seems extremely arrogant and counterproductive to shout "Wrong" and "misuse" when obviously pixels per inch has always been called dpi. And still is, and will continue to be. That is simply the name that is used and has always been used. It is so much easier to just accept that it is used, because it obviously is used.
Saying PPI is fine too, no problem at all with ppi, that is indeed what it means. The use of ppi is growing, but it remains a small minority. Some photo editors have changed their term to ppi, but there is no rule, and others continue to use dpi. But whichever they use, and whichever we prefer to see, we absolutely must understand it either way, ppi or dpi, because we absolutely will hear it both ways. It is very much like the word "set" too, we need to understand the usage context determines the meaning.
I do not argue about which is "correct". Both are correct. Ppi may be more clear to newbies, use it if you wish, but the name of the term has always been dpi, and it is fully correct too. Always has been.
I only argue that both terms are in fact used with the same meaning. We need to know that.
The point being that the only correct answer to such questions about "which" is that it is called both dpi and ppi, either one interchangeably. The only correct answer is "both". So just pick one, either one, your preference, and use it yourself, but understanding that both are used is essential, or else we don't know much, and we will remain confused since the rest of the world uses both interchangeably.
WHAT IS IMPORTANT is that beginners need to know the two terms are used interchangeably everywhere, with both terms meaning pixels per inch, simply so they can understand most of what they will find to read about the subject of imaging. There is no reason to confuse them even more by telling them everything they read is wrong.