These two subjects are so closely related that it is nearly impossible to discuss them separately, however they are different and each impacts an image in its own way.
Contrast derives its importance from the way the brain and eye work together to view the world. As I discussed here the eye does not see the whole but rather jumps from one key area of an image to another and the brain smooths over the gaps. In general the eye instinctively jumps to the point of the scene with the highest contrast and as such white against dark grey or black is extremely powerful whereas a lighter grey against a darker grey would be more subtle. A knowing photographer can use this to manipulate contrast and guide the viewer’s focus to wherever he or she desires.
In very general terms high contrast gives an image ‘pop’ whereas low contrast is gentler. Each one has it’s place depending on what you are trying to express in the photograph. For example if you were to be photographing dancing or sports you might want to make the images quite contrasty to add a sense of excitement whereas if you are photographing children or a family portrait then you may want to lower the overall contrast to add a sense of gentleness and peace.
It is very important to realise that the tonal range of an image has no relation on the contrast. Take these examples:
This first image has a tonal range of white to black however it would be considered a low contrast image because every tone is next to a tone that is imperceptibly lighter or dark. There is no contrast here at all.
This second image has an identical tonal range to the first one however; the leap from black to white is the strongest contrast possible.
Thus image contrast depends on tonal juxtapositions, not tonal range.
A tonal range of an image can generally be described as either ‘high key’ with light tones predominating or ‘low key’ darker tone more apparent.
Each approach has its own resonance and there is a strong emotional distinction between the two of them. In very general terms darker tones lead to sombre images whereas lighter tones are more optimistic. Of course there are many exceptions to this but it is a good place to start.
As a final word of warning I have seen many photo’s hurt by inappropriate contrast. There seems to be a fixation, in particular with beginners, to massively overcook the contrast in their images believing it to be an easy way to create dynamic photography. It is always worth considering what you are trying to say with an image before you push up the contrast slider in Lightroom. Will it really benefit from the muddy blacks, bright whites and destruction of the middle greys? Probably not.