There are many differences. First off, lets take a look at a manual for the construction of one of these kits, it will really give you a good reference. I will show you the instructions for a HG a MG and a PG. We will look at the head of a Zaku II, as an example.
HG, look at the upper right of the page to see the head construction
MG, look at the bottom of that page, and top of the next
PG, the whole left page
Now, after taking a look I will explain it simply. HG smallest kits 1/144 scale. The armor is not removable, it does not have an inner frame for better posability. you will find a better variety of kits for this scale though.
MG is 1/100 scale, is about a 1/144 + half of a 1/144 kit in size, generally speaking, some are bigger, some are smaller. The kits have an inner frame, which allows the armor to be taken off and on at will as well as cockpits that open. The mono eyes on the Zeon kits can move, normally back and forth, the Water kits, and Zeong for example, can move up and down as well as side to side. The latest Zakus, the 2.0s have a mechanism that turns the eye as the head turns from side to side, letting the kit virtuially look behind itself. They are generally more detailed.
PGs are 1/60th scale, they are about a foot tall. They are extremly detailed. The inner frame can be displayed without the armor and it will be impressive if painted correctly. The posability is slightly LESS then a MG because of the weight of the kit. One of the biggest Draws of a PG as you can see in the instruction, is that it has LED parts that come with it, to light up the mono eye, thrusters, and a variety of other things.
There are more types then this though, there are no grade/FG they are very simple kits, limited detail, limited part numbers, they are extremly cheap, and good to practice on.
There are Hg 1/100 kits, like the endless waltz kit.
HGUC is a high grade line, the newer ones have amazing tooling, some rivaling MGs in quality. This is compared to normal HG kits which you can find for the gundam wing series, G gundam, Gundam seed, and that ilk.
There are the vintage kits, which range from 1/144 to 1/60 but have very limited mobility and detail.
There is the HG mechanics series, which is a series of 3 1/550 mobile armors from the 0083 Series.
Also there is the Glorious scale kits, they are 1/60. They have no real inner frame like the PGs but they have an extreme amount of LEd lights, one for every thruster, camera, and weapon lense. The frame meerly supports the kit and houses the LEDs, there are only 3 of these, 2 Doms and a Gouf.
This is just a small cross section of the kits and series, I hope it helps.