HDR is High Dynamic Range. It is creating a photo that has a higher dynamic range than your camera sensor is capable of capturing in a single shot, and exposure. It can be created by taking three or more differently exposed photos and using HDR software to combine them, or use one photo and process it to three or more different exposure levels.

Blending is using more than one photo and masking certain sections of of each to create a photo that is made up of parts of each photo. So the sky from one frame and the foreground from the other.

Tone mapping is a process that is often run on photos to 'map the tones' in the photo. It 'standardises' the contrast across the photo, while retaining colour and detail.