When considering desirability, and the value of the diamond, clarity, plays a large part.  Still, this vital aspect of the diamonds grade, is not as straightforward as it might seem.

Clarity in Colorless and Near Colorless Diamonds
Diamonds are graded for clarity, based on the presence of imperfection within, or surface imperfections. Without question, people value a diamond with less than perfection more hence its price. 
A lot of people think an SI2, is a "worse" diamond than a VS1.

How important is clarity? For the purposes of this conversation, let's pretend that all the diamonds we are talking about are really well cut. Let's further pretend that all the diamonds we are talking about have no "brilliance issues"- that none are inherently dull.

The nature of the imperfections in a diamond does not affect the grade. That is to say, if a white imperfection, and a black imperfection are exactly the same size, they will likely garner the same grade from GIA.
DIamonds are graded for clarity based on the presence of imperfection- as opposed to the visibility of imperfection.
If there is a black spot in the diamond, and it is tucked away near a corner or under an angle where you cannot see it, the diamond might be graded SI2.  To the naked eye, this diamond could be identical to an internally flawless. In this case, the diamond is blocking virtually no light from leaving the diamond.
Let's say we move that black spot in the dead center of the diamond.  Right above a large facet.  Now you can see the imperfection with the naked eye.  The diamond would still be graded SI2, if the imperfection was exactly the same size as the one in the first example. In the second case, the diamond is not eye clean.
For this reason, it is not possible to say that every SI2 diamond is not eye clean, or that every SI1 diamond, is eye clean
An imperfection GIA grades SI2 is not large enough to impact the overall brilliance of the diamond.  This is also true for many imperfections graded I1 by GIA.

Clarity plays a direct role in the pricing of colorless and near colorless diamonds. Still, it does not stand on its own.  That is to say, and internally flawless diamond that has a bad cut is a very tough item to sell-therefore it's worth a lot less than a well cut internally flawless diamond. Cut always plays a large role.

In Fancy Colors:
When considering fancy colored diamonds, the actual hue, and intensity of the color are generally more important than the clarity. 
There are a lot of reasons for this.  For one thing, the body color of the diamond tends to hide imperfections.
Mainly, I think clarity is less important in fancy colored diamonds, because the ultimate color is what you are looking for.
For example, many pink diamonds are from the Argyle mines in Australia.  Diamonds from that region are generally not clean diamonds.  When looking for an intense pink, or a vivid pink, you will not generally not find VVS or internally flawless stones.

A 1.00ct diamond graded by GIA as Fancy Intense Pink, SI2, might be worth $500,000

The show the effect of imperfection let's will use this 2.02 Pear Shape diamond graded "Fancy Brown Yellow" by GIA.


Here's a look at the 2.02 in a photo that really shows the imperfection....on the right I've outlined the imperfections


There's actually only two imperfections - but it looks like there's more.
How is that possible?
The area outlined in Green is a "white feather" which runs at a diagonal in the "up and down" axis. It's starts near the edge of the stone- but it actually is situated inside the diamond.

The next area of imperfection is outlined in red- this is a carbon spot.
Oddly enough, the areas in blue are both reflections of the one carbon spot.
The carbon is located beneath the table- but right at the edge. This causes some weird light tricks.
What happens is that the facet directly to the left of the table grabs the light from the same area of the diamond which includes the real estate below the table- right where the black spot is.
The small blue area in the center is yet another reflection of the blot....

Well - I think a photo will never tell you how to grade a diamond. It will help to figure out how visible any inclusion is, though, and I think of the two this is by far the most important.

Important too - if there was a plot of the imperfections on  the GIA report ( there is not)- it would only show the imperfections- not the reflections of them.
In this case, the report would make the diamond seem less imperfect than it is visually.
Of course, the opposite can be true in many cases. What seems like a whole lot of junk, and the diamond is gorgeous eye clean.

The point is, it's really impossible to say how a diamond will look based solely on the plot on a GIA report.

  There is no difference in how clarity is graded. There is a significant difference in the extent to which clarity grades impact price... but the grading scale and process are the same.