Most points touched on here (didn't look at the Wiki, maybe a lot more there)... the key process difference is HA-II is done at "room temp" (roughly 68-72F is ideal) and modest current levels (12 amps per square foot I believe is the average standard number, but don't quote me on that). HA-II and HA-III BOTH grow into the surface, however HA-II is roughly a 1/3 to 2/3 ratio (1/3 in, 2/3 out), so it's not as deep as HA-III which is a 1:1 ratio (1/2 in and half out), and also HA-III allows thicker overall layers, although HA-II can get pretty thick as well if done right.
Related to the above "growth" effects is the pore size, basically either version makes "cells" of aluminum oxide which resemble hollow tubes or a "honeycomb" effect... HA-II has larger pores which allows more colors to be used to color the final product (dyes have different particle dimensions depending on color used, etc). HA-III has smaller pores, which means only the finest particle dyes can be used, which are the green and black basically (there are other types of anodizing where the anodizing process itself makes the material appear either gold, or "shimmering" depending on method, I won't go into that much detail here).
Now onto HA-III, it is done at a much cooler temperature (sub-50 degrees bath temps), and at a MUCH higher current density (30-70 amps per square foot or something like that, it's been awhile since I researched it). It is also done with a much lower concentration of acid (about half of HA-II I believe, which is around 19-23% by volume, so around 8-12% by volume for HA-III). Basically by reducing the acid concentration and temperature, the newly formed oxide layer is attacked much more slowly by the acid, and in conjunction with the much higher current, can penetrate more deeply into the base material and extend out farther as well. But the high current requirements, and the other stricter requirements (each anodizing shop guards their specifics pretty well as each has their own recipe) make this much harder for "DIY" HA-III. You need a very well controlled current source (hitting an "on" switch would likely burn any connections to the part due to the sudden voltage and current spike and bring a quick halt to any effects), typically this process is ramped up, regulated, and monitored for specific "end of process" effects (voltage changes, current changes, etc). Just not easily replicated at home, you could do it for something very small (an aluminum locket or clasp maybe) if you had a 3-amp power supply, but if you even have a 1/2 sq ft surface area (reasonable for a flashlight for instance), you'd need at least 15-30 amps of current, regulated, and the other requirements. Best to find a shop that can toss it in with their other jobs.
or not.
