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The Dodge and Burn tools are used to subtly lighten and darken areas of your photograph. This is most commonly used to improve the contrast of specific areas (as opposed to the entire photo). An easy way to remember which tool is which is to think of “burning” as in burning toast, making it darker. The effect is subtle, but if you paint over the same area a number of times you can gradually make it more dramatic.
Cloning on the other hand is copying one area of your photograph to another. You select a “source” (by clicking on your photo), then paint onto the “target” (by clicking and dragging). This basically “clones” (or copies) the source area onto the target area. This is particularly useful when you want to remove an object from a photo – you can clone a nearby area over it (for example you could clone a wall over a person you wanted to remove). You can also use it to duplicate features of a photo, such as to add more clouds to a sky by cloning an existing cloud.
Let us know if you have any other questions!