High Dynamic Range Imaging (HDR) has been around in one form or another since the 1850s. Gustave LeGray took multiple exposures of seascapes and combined them to render both the brighter sky and the darker water/seashore in the same print. In the mid-20th century Ansel Adams and others used dodging and burning, or what we call manual tone mapping, to raise the technique to a high art form.
Unfortunately, most people seem to think HDR means only the recent development of making a high-dynamic-range luminance or light map from multiple digital images exposed at different values using only global image operations (across the entire image), and then tone mapping this result. This type of digital global HDR was first introduced in 1993 resulting in a mathematical theory of differently exposed pictures of the same subject matter that was published in 1995 by Steve Mann and Rosalind Picard.
What is known today as Digital Blending is one way to accomplish High Dynamic Range Imaging.
- Digital Blending takes different parts of several varying exposures of a scene and uses the properly exposed parts of each to create a new image in such a way that different parts of the scene that would be too far apart dynamically to display in a medium of limited dynamic range (such as a computer monitor or print) can be displayed in the limited dynamic range of that medium. It does so without creating a large floating-point file and the resulting need for tone mapping.
- Another way to do High Dynamic range imaging is the process commonly referred to as HDR that has evolved from the work of Mann & Picard described above. It makes a high-dynamic-range luminance or light map from multiple digital images exposed at different values using only global image operations (across the entire image). The result is often a 32-bit floating point 'image' that no monitor or printer is capable of rendering. (Even when you open a 12-bit or 14-bit 'raw' file in your photo application on the computer, what you see on the screen is an 8-bit rendering of the demosaiced raw file, not the actual monochromatic Bayer-filtered 14-bit file. As you change the settings and sliders the 'raw' data is remapped and rendered again in 8 bits per color channel). It must then be tone mapped by reducing overall contrast while preserving local contrast to fit into the dynamic range of the display medium. This often leads to artifacts in the transitions between areas of high contrast.
- There are an almost countless number of other processes used to produce High Dynamic Range Imaging, including those used in the analog (film) age of photography.
Each technique uses different approaches to the problem of a scene with more dynamic range than our current technology can reproduce using conventional techniques. Which one, if any, you choose to use should be based on what you wish the final result to look like as well as which fits your workflow the best.
See the halo around the balloon in the picture below? That is the result of global tone mapping of a single exposure to make the much darker balloon closer in brightness to the brighter sky. If I had used other techniques, such as digital blending, exposure fusion, or even manual cut and paste from different layers developed at varying amounts of brightness then the sky would remain the same brightness all the way to the edge of the balloon but the boundary between the sky and balloon might look like the balloon was cut from another picture and pasted onto the picture of the sky.

For further reading:
http://en.wikipedia.org/wiki/High_dynamic_range_imaging
http://en.wikipedia.org/wiki/Tone_mapping
http://en.wikipedia.org/wiki/Zone_System
http://en.wikipedia.org/wiki/Dodging_and_burning