Photoshop :: Output Color Difference

At the core of it all: "images from PSD exported as a .png, or a .jpg (commonly for me) do not show the same...contrast or fidelity my photoshop-canvas shows me..

I have been working on some stuff, and quite some time ago, I noticed that a certain piece of mine was not showing the subtle, noise-fog that I had added in PSD.Now, on-canvas everything seemed fine and I thought: "Okay, This is what I want." However, when I saved the image (as a .jpg and later as a .png as well), the fog was absent from the image, showing simply a "black" background. Sometime later I found that, when I zoomed in, the noise was actually present, it was just VERY unclear. You could only notice it, just barely, whilst zoomed in.

Now we come to present-time. I'm working on a little concept. It's in manga cell-shaded style, so the differences in color are easy to see (as shadows, for example, are not gradual. There's a clear line that separates the normal lighting from shadows)

Now, this 'character' has a black pair of pants (specific RGB- #100d11) and the color of the shadow is #060506..The thing is: in photoshop, I can clearly see the difference and it looks the way I want to have it. But when I saved the image to jpg (and to png) you can barely, if at all, see the difference. Someone who does not know there are two different colors, would not see it, and just see pure black. You can see the difference if you zoom-in, but even then it's not as 'stark' as it is on-canvas.

- Is this common / normal?- If yes, is there something to fix this, so that what I see on-screen is what I get when I export the file?