what's the difference between spatial and temporal characterization in terms of image processing?

Temporal characterization occurs when you have a series of images taken at different time. Correlations between the images are often used to monitor the dynamic changes of the object.

Spatial characterization applies when you are analyzing one image. It includes but not limited to the coordinates, intensity, gradient, resolution, to name only a few.

Check this paper on blood vessel analysis to get more details among the two.

Spatial = Space Example, Image consist of pixel values which needs memory space to store. Spatial information = Pixel values stored into Memory
Temporal = Time Example, Video consists of image frame sequence. With respect to time the frames are changed in video. This is called Temporal Information.