Tone mapping is using an algorithm for one of a couple of different purposes. You can use it on a single image to increase the contrast on a photo and possibly give it the look of an HDR photo, but only if the difference between lights and darks isn't too great. If you use it on a single photo with too many lights and darks, you simply won't capture the detail that an HDR photo will.

The reason why an HDR photo WILL actually capture those details is because it's an amalgamation of (usually) four to six photos taken in sequence from under exposed to over exposed. Photoshop is used to stitch together all the different properly exposed areas of all the different images into one image that has all the perfect exposure levels for all the light and dark areas. I know this is confusing, but tone mapping can also be used during the stitching process to create an HDR photo.

So, HDR = multiple exposures stitched together
Tone Mapping = algorithm used to emulate the HDR 'look' on a single frame, or to help during the creation of proper HDR images from multiple frames.

Please view the two sources below if you'd like to get an even more detailed explanation.
Source(s):
http://en.wikipedia.org/wiki/Tone_mapping
http://en.wikipedia.org/wiki/High_dynamic_range_image


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