"Photoshop" is a good shorthand word for the process. People know what you mean when you say it. I remember the glory days early this decade when "PHOTOSHOP FAKE!" became a known term on the Net. (Warning: don't Google the phrase. The first hit I got was 9/11-related. Warning done.) At first Photoshop was just an apt name chosen by a programmer, most likely, to name a program, but it grew and took on more significance. I know from bad names -- I've heard of the Zune -- and a bad name can be confusing. What is this? What does it do? "Photoshop" is a functional word. Maybe at first blush someone might think it's a way of selling photos, but at some level you can then think of shop class where you can make stuff and so maybe "Photoshop is like 'making photos'" and it quickly becomes clearer. And that meaning gets reinforced, the way "Google" has become another useful term. "Photoshop"'s been getting reinforced for much of this decade.
Photo manipulation has been around as long as photos. It's spawned other shorthand terms for said manipulation. "Airbrush" comes to my mind; that was a literal tool one could use on a photo to change it. (I think I first heard the term "airbrushed" when David Gerrold's The World of Star Trek recounted how one of the earliest released photos of Spock was airbrushed to get rid of his pointed ears and eyebrows. Someone with the production, the studio or the network had gotten nervous about the potential "demonic" connotations of Spock's look -- that someone almost certainly had not read Arthur C. Clarke's Childhood's End, come to think of it (or C.S. Lewis's That Hideous Stength, too) -- and had had that photo redone. Gerrold said that this resulted in some poor airbrush artist almost getting fired, "and all he'd done was follow orders no one would admit to giving!") There could be an unreal quality to airbrushed photos, though: they could look like they lacked substance, because really, all that was being done was ink was getting sprayed around, and spraying is hard to do precisely. (Or maybe I've just seen bad airbrushing.)
You also could tint photos, adding colors on top of the image. That was popular when black-and-white photography was most viable -- though people were experimenting with color photography early on, with fascinating results -- but what could you add to the image by tinting? It didn't change shapes; it could mainly change emphasis, changing what your eyes were drawn towards. Color overlays to add or change color really just changed emphasis at most, as well; it wasn't really that elaborate an effect. Photoshopping can be. You can do all sorts of things with it. Whether the manipulation is obvious or not can vary (artistry's again involved, and like with different eras of movie special effects there's almost always some "tell" that shows the image's been manipulated*), but the possibilities that technology gives us have implications beyond what I feel informed enough to write about here.
Photoshop. A useful name for a useful process. I'm not up for talking more about that process, how it can be both used and abused, but I can think about language.
* When I heard people complain about CGI effects looking fake, I want to say "And matte paintings don't? Or blue-screen or green-screen effects? Or those black lines and vague translucent squares around spaceships in the original version of Star Wars? Or stop-motion animation like what Ray Harryhausen did?" Different effects have different "tells" showing that they are effects, and at some level we notice them. We're mainly not used to seeing CGI, so such "tells" might stand out more. Plus there's plenty of bad CGI effects work, whether from too little money or too little time being spent.