Please note that the idea of axes is something that I came up with on my own and is in no way sponsored by any other builder (Although another could have come up about it or something like it separately). If you see a flaw in my logic, please comment.
Anyone familiar with Dungeons and Dragons is probably well versed in the idea of axes (The plural of axis) that can say something about a character's personality. In version 3.5 (The only good version, in my humble opinion), one axis is lawful and chaotic and the other is good and evil. There is also a neutral option for each axis, creating a grand total of nine different positions on the axes. The same is true for MOCing styles. The two axes that I have observed are custom and standard as one and Hero Factory or Bionicle as the other.
Let's start with Hero Factory vs Bionicle, since that's probably what most people are most knowledgeable about. By Bionicle I mean building using pieces released in-between the Throwbots of 1999 and the first wave of Hero Factory in 2010. Bionicle style of building uses a lot of different ways to connect one piece the the other, such as axles, gears, studs, ball-and-socket and thin rods. It allows a lot of variability, but on the down-side it can be confusing with so many different connection methods all tangled up together.
Before the second wave of Hero Factory, all MOCs were Bionicle style, since the newly released Hero Factory sets were essentially Bionicles. The second wave changed all that, introducing a whole new set of pieces that worked very differently than old sets. Hero Factory style uses almost entirely ball-and-socket building, with a basic thin skeleton made up of ball-and-socket bones covered with socket armour. This is the only style of building available to you if you don't already have some bionicle pieces and don't want to buy Technic sets or older sets. The up side is that it is simple and clean, but it is also harder to do something out of the ordinary with Hero Factory pieces since there are only 3 years worth of pieces compared to the eleven years of Bionicle pieces.
That's a lot of writing, so here are some pictures. This is an example of a purely Bionicle MOC by Ben Cossy, entitled Makuta Septerra.
The MOC is by Ben Cossy. Note how the pieces come from a variety of set-years (2003 or earlier to 2010) and the shape is non-humanoid. Non-humanoid shapes are also possible with Hero Factory, but it is arguably easier to do it with bionicle parts. Now here is a fully Hero Factory model called Jetbug Revamp also by Ben Cossy.
Okay, so a revamp probably wasn't the best example to illustrate my point, but it's hard to find purely Hero Factory MOCs since most builders go for mixed Hero Factory and bionicle. This isn't completely Hero Factory itself, as you can see from the 2003 translucent orange pieces. But it pretty well shows how most Hero Factory builds go. Notice that the armour on the arms, legs, torso, and jet boosters is mostly in bigger pieces and the build is as humanoid as a bug can get. Here is a look at a mix of Hero Factory and Bionicle pieces by Callan Lof. The model is called Obseshin.
See how the arms and legs mostly use large pieces connected by ball-and-socket systems but the other parts, the weapon and torso especially, use other techniques to connect everything.
Since this post is long enough as it is, I'll talk about standard vs custom in another post. In the meantime, here's some building challenges.
Beginner: Build a model using Hero Factory while connecting the pieces, but try to use other connection systems at least as much as ball-and-socket.
Intermediate: Build a MOC using hero factory bones but Bionicle pieces for the skeleton.
Expert: Build a MOC out of Hero Factory pieces, then another out of Bionicle ones. Make the two models have the same color scheme, height, weapons, body type, everything except the type of build.
Boss challenge: Build something large and high-quality with only pieces available in models this year. Try to keep a consistent color scheme and make it at least two feet tall.