14th
Aperture - Levels, Exposure and Curves
The exposure slider in Aperture does pretty much the same as moving the right bottom sliders in Levels. One difference is that one naturally can move the right slider in levels only to the left. The exposure slider can be moved in both directions.
The brightness slider does the exactly the same, except that it acts on the left bottom control in Levels. The contrast slider acts on both the right and left control.
In general, Levels is a much more powerfull tool [than the Exposure section] but can be trickier to use (and it is easy to spoil an image by making it look unnatural). Its sliders can create much more drastic changes, e.g. extremely high contrast. And by offering midtone and quartertone controls, different tonal ranges can be adjusted differently. By moving the top sliders the these controls can be moved to any point in the tonal range.
When moving the right or left slider in Levels to the start of the histogram (to create pure blacks and whites), particularly when moving them quite a bit, one often might get better results by doing this separately for the three channels than on the luminance channel.
Generally, I have the impression that Exposure/Brightness/Contrast do a better job at balancing the three colour channels than the levels adjustment set to Luminance to maintain a natural look.
Comparing with the Curve tool (in e.g. Photoshop), one can state that levels and curves do exactly the same, the top controls on the diagram in levels in Aperture are the output of curves (y-axis) and and the bottom controls in Aperture are the input of curves (x-axis). The level controls in Aperture, however, ‘only’ have five control sliders at the bottom and only three at the top (and none at endpoints there).
An attempt to explain why all controls do more or less the same:
Take a B&W image (that makes things easier to understand). Any global image manipulation does nothing but remap luminence values. Every lumininence value in the original image gets translated into a value in the output, e.g., adding 20 (on the scale 0-255) to all brightens an image (probably not in a very smart way). This remapping is given by a functional relationship that can be illustrated by the curve in Curve tool. But there a lot of ways to represent that functional relationship, with levels being just another one (and one that I find more intuitive).