Is there a difference between exposure and shutter speed, or are the terms interchangeable? I read that "If you use a quick shutter speed, you can just raise the exposure to compensate." Is this statement invalid, or is there a difference?
The term "exposure" is used for a number of different but related things in photography. I can see how this might be confusing. Here are five different ways in which it is used:
Exposure value is a common technical term which uses the first sense in the list above. You can read more about that in the question What is the EV scale?.
Confusion between sense #1 and sense #2 above sometimes results in long, pedantic flamewars between people who both think the other person is wrong, and don't realize that they're actually talking past each other.
In the example sentence you give, "If you use a quick shutter speed, you can just raise the exposure to compensate", I think the term is simply accidentally misused and that they probably meant "ISO sensitivity". Raising the exposure (or exposure value) doesn't really make any sense in that context.
Exposure is a combination of three things:
Aperture - the size of the opening in the lens through which light passes
Shutter Speed - the time which the sensor is exposed to the light
ISO sensitivity - the sensitivity of the sensor to the light it is exposed to.
So there isn't really a difference between shutter speed and exposure, but it's part of what makes an exposure.
In the text you read, when using a faster shutter speed, the sensor won't have so much time to "see" the scene, so you might consider using a larger aperture (a smaller f stop), or increasing the ISO sensitivity of the sensor, to compensate.
I am still researching this topic, because in no place i can find information about shutter speed. Speed is a function of distance vs time, while the shutter controls only time. We don't know the actual speed pf the shutter mechanism, nor we have to care about it. So i think the technical figure is "time of exposure" and that shutter speed is an arbitrarily one.
Photography is all about exposure, both in experience and light captured. When you heard:
They may have been referring to Exposure Value.
As stated before, you can change the exposure in a few different ways. Most basically Aperture and Shutter speed. Assuming you know what both are, you can shoot in aperture priority or shutter priority. Or fully manual where you control both. You also can change the EV (Exposure Value).
If you can manually change the aperture and shutter speed to control exposure, why bother having EV?
Well, in aperture priority, changing the EV actually changes the shutter speed (or ISO) accordingly. You might want a particular Depth of Field.
In shutter priority, the EV value will change the aperture (or ISO) accordingly. Again here, you might want a blur effect where the DoF doesn't really matter.
And again, ISO changes the sensitivity of the sensor. In the film days, a roll of film was graded with an ISO value. Most commonly 100, 200 or 400. So it's great in this digital world you can just press a button!
A low ISO value means it's not very sensitive to light so you can have a brighter exposure. A high ISO value means it's more sensitive to light, so you can have darker exposure. But, the higher the ISO, the more grainy the results.
Briefly, exposure is a combination of factors all of which together tell you how much light accumulates on the sensor to make the picture. Shutter speed is only one aspect of exposure. The three major factors are ISO (sensor or film sensitivity), f-stop (how much light the lens lets thru), and shutter speed (how long the light has to accumulate on the sensor of film).