Note: This answer was merged from a question that was almost identical to this one - the only difference was a minor focus on ethics, which is what I tried to explain in the second part of my answer.
This question is one for philosophy-courses and is therefore open-ended and purely opinion-based. Therefore, it will be hard to answer it at all - more so if I want to make it factual and less a piece of opinion. I have learnt about all the things below in philosophy-in-media courses - mind you, I'm not someone who likes to follow someone else's philosophy, so I have no citations; if I find some, I will offer them, of course.
First, a disclaimer: To me,
Therefore, I think it is not really possible to differentiate between the four - one might say that "enhancing" is something like de-noising, that "retouch" is something like cloning away a pimple, and that "editing" is something like compositing (i.e. adding persons from other photographs in your current photo); but still, they all are just forms of manipulation.
1: What is manipulation?
And already, there is no straight answer on the horizon.
Some people would argue that we manipulate the image in the moment we look through the camera - as we clip away unwanted stuff outside the framing, and even more so because we take something three-dimensional and make it two-dimensional. Also, cameras do not work like the human eye (which in itself manipulates the real world) at all, so...you get the idea.
Other people - like me - see it that way: A photo tries to be an accurate representation of the world as hard as it can - at least if you take a DSLR and capture in RAW. Sensors are not made to manipulate the image - they work within the boundaries that physics set. Also, taking a photo does not manipulate any more than if you point at something with your finger and say "Hey, you! Look over there!" So in this philosophy, manipulation cannot be done by framing alone.
Then, there are the questions of exposure times and multiple exposures (not the same as HDR!)
Image stolen from some blog - really, I just DuckDuckGoed "Marubi".
See the ghost-curtain in the above image? That is the kind of multiple exposure I am talking about! It is from one of the Marubis - Albania's first photographers. (I can really recommend the Marubi Museum in Shkodra ;-) ) The picture itself is quite old - the Marubis worked somewhere between the late 1800s and ca. the 1950s. It is a simple matter of exposing the same film multiple times - clearly, some kind of manipulation!
...or is it? Some people would still say "no!" - and I'm one of them - because to them/me, manipulation begins when someone cannot possibly spot the manipulated object as such. I know, this is not a consistent argument. ;-)
The same goes for long-time exposures:
Image stolen from Krisztian Birinyi.
Have you ever seen a tram that is made out of lights alone? Me neither.
There's a lot of other techniques that will produce "manipulated" photos - be it black-and-white, be it over-/underexposure, Infra-Red, Tilt-Shift-photography, etc.p.p. - all above applies to those, too.
So as we see, we do not even have a clear definition of "manipulation" - it could be as trivial as "everything", as well as "everything behind the exposure (if we take a neutral picture without filters, properly and only once exposed at a decent shutter speed of 1/25"-1/125")" to "manipulation must be invisible to be manipulation".
When you have set yourself with your own definition of "manipulation", the next question awaits you:
2: Is there a red line, morally speaking, for editing?
And again, there is no simple answer.
First, I will go with the example of fashion photography.
Image stolen from Untitled Magazine's article "Photoshop In Fashion - The Times Are Chaning".
Psychological studies revealed that the heavy use of Photoshop in the fashion industry is a major factor for anorexia: making the (usually already quite thin) models look like they only weigh half as much as my left leg certainly does influence the perception of the own body.
Therefore, some countries try to regulate this: They either ban photoshopped pictures (if they manipulate the body-shape) or they at least require a visible disclaimer about it. France is one of those countries, and as far as I know, the UK is another one. Getty Images followed the French law later on..
Still: If you want to keep the picture to yourself, it would be absolutely okay to make yourself as thin as a piece of toast - both morally and legally.
Other people I know - I do not want to make it political, but most of them really have a overall liberal attitude - think that morally, there is no problem with any kind of retouching. In their opinion, everyone is responsible for their own perception, so there is no need to have labels, regulations, or even moral debates about a red line in editing.
Really, it comes down to opinion and what you do.
As Corey pointed out in his comment, there are of course differences between different types of photography, e.g. creating a fashion ad, an art-for-the-art's-sake project, and photojournalism. While it is okay to heavily manipulate an art project (even beyond recognition), photo journalists would (and should, in my opinion) stick to very basic editing - after all, journalism should be as objective as possible*.
* The question of "how objective can journalism be?" is a bit too lengthy and too off-topic for this answer.
I, for one, tried to avoid Photoshop (and even de-noising!) for a very, very long time - not because I disliked photoshopped pictures, but because it was my choice of style. Later on, I started to "repair" minor mistakes - red eyes, slightly open mouths, pimples,... . Much later on, I started to shoot portraits semi-professionally - and with that, I started to get into the whole business of brightening, softening, and what-else-there-is in retouching. I am still happier to have an almost-perfect photo straight out of the camera than a perfect photo out of Photoshop, plainly because photography is a destructive process, while photoshopping is not, and therefore, photography is a damn lot harder. What I really try to avoid is the above mentioned weight-stuff: I never made anyone look any thicker, slimmer, taller or smaller than they are; I simply despise the idea.
I know a lot of people who liked my initial approach and who are not very pleased with what I do today - and vice versa. It is the same when you look at basically any platform, be it flickr vs flickr, 500px, etc. (Except of course Instagram: that is as much manipulation as possible).
...And do I use Photoshop a lot? No. Most of the time, I simply clone a few things away, fine-tune exposure and white-balance (all that C1 can do from within its "Quick"-Panel) - but no ground-breaking compositing. That is something I only use when absolutely necessary - simply because it is an extremely time-consuming process.
At this point, you will most likely be disappointed, because I have not answered your question at all - I am sorry for that.
I can offer one definitive solution: Keep the original file - and be honest about your work. If you think about something as being objectionable, tell people about it: Post it in the photo's descrition, maybe add a link to a thumbnail to the unedited picture. I certainly would not do so as long as I just "clone away" unfamiliar people or blur away a pimple - but that certainly is something that is up to you.