Here we go as I understand it.
Start with frequency wild.
It does exactly what it says on the tin. Generally this will be an alternator which is physically connected by some direct drive to an engine. When the engine speeds up the rotor in the alternator speeds up giving a higher frequency AC supply. Vice versa when it slows down, the frequency slows down and therefore reduces. As a result, it is described as frequency wild and is unsuitable for complex electrical circuits which could be damaged by significant frequency changes. "Untreated", this AC is generally used for electrical heating due to the fact that heating elements are not as sensitive as other equipment.
Stable AC (if I recall correctly!) is simply Altternating current which is stable in frequency. It is typically produced by an inverter or an integrated drive generator (IDG).
An inverter electronically creates AC from a DC source and so the frequency, and voltage can be readilly and accurately controlled.
The IDG is a generator which is connected to and engine by a variable gearing system, frequently a self contained hydraulic system, which maintains the generator speed at a constant regardless of the speed of the engine it is connected to.
The advantage of stable AC is twofold. By having a pre-determined frequency, voltage and phase it can be used for a wider variety of purposes than frequency wild AC. Secondly, and although not often used due to the complexity, stable AC can be matched in terms of frequency and phase in order to be combined.
Hope this helps a little,
Obscop