1. Contrast: yeah, shades of gray.
Pure White .... shades of gray .... Pure Black
If you have one thing at pure white and one thing at pure black, these things have the greatest contrast. As the distance between the things on this continuum gets smaller, there is less and less contrast between the two.
2. Dynamic Range: has more to do with lighting and capturing detail than actual contrast
You are inside a room looking out an open doorway. To your eyes, you can perceive great detail in both the inside of the room and the outside world past the doorway. This kind of scene has a pretty wide dynamic range; you've got your really bright stuff outside and your dimly lit stuff inside. Since your eyes are able to capture a very wide dynamic range, they have no problem perceiving detail in both the dimly lit and the brightly lit all at the same time.
Camera sensors don't have this wide range. If it tries to get good detail in the bright spots it won't record detail in the dimly lit areas. If it tries to get good detail in the dimly lit areas the bright areas bombard the sensor with too much light and you get a detail-less white area. This is due to the sensor site's well depth and the light sensitivity of the sensor. Perhaps this is best illustrated with an example.
Light sensitivity:
Say that you have a sensor site that requires at least 50 photons to be able to capture some sort of detail. If you give it something like 30 photons, and all it does is capture black, or captures noise.
Well depth:
This is how many photons the sensor can hold before detail is lost. Say you have a sensor site that's deep enough to hold 500 photons. At 500 photons and above, the sensor site starts to overflow with photons and it just captures detail-less white.
So you have a sensor that can capture detail as long as it's given between 50-500 photons of light. Below 50 photons, all it records is black. Over 500 photons, all it records is white.
Back to the room with the open door example:
Per second, the bright part of the scene (the outdoors) is sending between 250 and 750 photons your way.
Per second, the dim part of the scene (the indoors) is sending between 25 and 75 photons your day.
Aha, we have exceeded the dynamic range of your sensor.
If you shoot at 1 second shutter speed, you lose detail in both your highlights and your shadows. In the bright part, you blow out the details that are sending 500+ photons to the sensor. In the dim part you lose detail in anything that is sending you less than 50 photons.
So you try and compensate by changing the shutter speed. You change it to 1/2 second.
In 1/2 second, the bright part sends you 125 to 375 photons. Hey, your sensor can capture all the detail in this bright part! Great!
But in 1/2 second, the dim part only sends you between 13 and 37 photons. Because the sensor requires at least 50 photons to record detail, you've lost ALL detail in your dim area.
In this case, there will be high contrast between the bright areas and the completely black dark areas.
You change shutter speed to 2 seconds.
In 2 seconds, the dim part sends you between 50 and 150 photons. Your sensor can capture all the detail in this dim part!
In 2 seconds, the bright part sends you 500 to 1500 photons. Because the sensor well is only deep enough to hold at most 500 photons, you've lost ALL detail in your bright area.
In this case, there will be a high contrast between the detailed dim areas and the completely white highlights.
Sensor dynamic range is 50-500 photons. Your eye's dynamic range is wider, say, 10-1000 photons, meaning it only needs 10 photons to perceive detail and can perceive detail up to a maximum of 1000 photons bombarding it. So a scene that shoots out between 25 and 750 photons is no problem for your eyes, but IS a problem for your camera.
Your eyes with a very wide dynamic range can actually perceive the scene as not having too much contrast. But your camera with its limited dynamic range will see the scene as having a lot of contrast because parts of the scene will either be entirely blown out to white or entirely black.