The "hallmark" smocking technique is called English smocking, its origin obviously attributed to England. This method, along with the smocking variations that have developed over the years are described briefly below. I included photos when I found good examples.
English (or Geometric) Smocking
North American Smocking
This style of smocking appears to have originated as a way to simplify the smocking process. Iron-on dot grids were transferred onto the wrong side of fabric and then used to create the smocking pattern as it was stitched (the dots could also be used to gather the pleats with a running stitch). First distributed in the 1880s, these patterns were very popular during the early to mid-twentieth century and were commonly sold by pattern companies.
A simply smocked base design is heavily embellished with embroidery stitches to create a decorative panel. The smocking itself becomes secondary to the extra surface embellishment.
With Picture smocking, embroidery stitches (typically cable stitches) are stacked to create images on the right side of the fabric. The back side of the pleats are smocked as well to fix the pleats in place so that they will not stretch and distort the designs on the front. This eliminates the ingrained elasticity of the general smocking technique.
This type of smocking is performed on striped, gingham (checked), or dotted fabric that is pleated while being embroidered, rather than prior to embroidering. The color pattern of the fabric can be manipulated to create designs by arranging the pleats to show or obscure colors to create bands or blocks of color. Counterchange smocking is static and not stretchy like English smocking.
Grid Smocking/Italian Shirring
This type of smocking is created by lines of running stitches that when pulled up, shift the fabric into patterns. It is a bit hard to describe, but you can see an illustrated example at the blog Bubblegum4Breakfast.
Lattice smocking is done on the wrong side of the fabric to create a pattern of folds on the right side. Stitches are taken both horizontally and vertically, affecting the dimensions of the fabric in both directions. Unlike the previously mentioned smocking methods, the stitches are intended to be invisible on the front. This method of smocking is particularly effective on heavier fabrics such as corduroy or velvet. This technique seems to be used more frequently on home decor items, specifically pillows, rather than on garments.
I hope that you have enjoyed this brief introduction to smocking techniques. I have been working on a counterchange smocked pillow and enjoying that very much.