Already with 7 answers to fly in all directions, I think it’s time to set up some straightforward words! Since many answers in the answer are about “retouching“, like Photoshop – whatever you can do with IMHO is not right. I believe some words may overlap with each other, but some may actually be quite specific.
Let’s define some terms a bit more refined, in relation to Photoshop’s glossary:
Extracting an object from its background, probably by using a mask.
Using several (parts of) images (as layers or selections) to construct a new image. It’s a highly creative task, which often requires an amount of talent, imagination and proficiency. We’re entering an experts and artists area!
Applying changes to an image that tend to creatively conceal or reveal things normally seen or unseen. These can involve cropping, scaling, distorting, brushing, cloning, warping, liquifying, etc. But as a general rule, one might say that these actions stretch far beyond what would be perceived from looking at the original image.
Make slight or dramatic adjustments, specifically in color, light, brightness, sharpness, etc. Again, adjustments can go further than what would or could be normally perceived from the original image. So from a certain point on, adjustments can also be considered as an intention to create an alternate image, to convey a different message.
And then we come to retouching, which can be considered as the more subtle approach to local image edits. One could say things which the photographer could realistically have done in preparation for taking the picture. E.g. removing distracting elements, applying or looking for a bit different lighting, preventing unnecessary inelegant shapes or even technical flaws. All done without conveying a totally different message or perception.
Another probing question might also help to know and judge about what people can do with software like Photoshop: to what extent can someone use a tool like Photoshop for journalistic, documentation, or even forensic purposes?
I hope this helps to distinguish the jargon a bit.