We've actually discussed this some on this site's meta, in attempting to make the proper distinction between tags photo-editingand post-processing.

See Are photo-editing and post-processing synonymous? and follow-up Are image manipulation and photo editing synonymous?

In short, in practical use, it's very blurry and there is a lot of overlap. From that discussion, though, let me show you the descriptions we've arrived at for various related tags:

• Post processing is the process (and art) of adjusting a previously-captured image to obtain a desired look. It encompasses everything from simple whole-image adjustments to detailed per-pixel touch-up work.

• Image processing is the computational transformation of an image signal. It's about the technical side of batch transformations, conversions, and enhancements, as distinct from post-processing (adjusting an image to achieve a desired look, probably using image processing).

• Photo editing is the process of reworking an original photo, either produced by film or digital, to create the artistic vision of the photographer.

You're asking about "image editing", which is none of the above, but I think we can extrapolate. Crucially, editing has at least some of the implication remaining from the actual job "photo editor" — see this description from Wikipedia:

... a professional who collects, reviews, and chooses photographs and/or illustrations for publication in alignment with preset guidelines.

So, in one sense, photo editing (and by extension image editing) are the things one might do along those lines. But, clearly, in common use, we also use it to mean "all the stuff one can do with Photoshop".

Likewise, image processing has implications of its own, this time of signal processing. Again from Wikipedia:

... image processing is any form of signal processing for which the input is an image, such as a photograph or video frame

So, from a technical point of view, the term image processing leans much more towards the technical side, and barely what humans do at all — as our tag definition above says. But again in common use, this is used very interchangeably, and if someone referred to their work in Adobe Lightroom as time spent on image processing, we'd all understand.