The direct answer to the question as it is ("What´s the relationship between AOA and Airspeed?") is simple: none whatsoever -- that is, until you introduce context and some conditions.
Your context is: we want an airplane to fly. And not just 'fly' but to keep level, at least. For that, you need a certain amount of lift. Lift is used to counteract weight, so you need at least that much to fly level. Plus, you'll need some extra to pull most manoeuvres (such as turns).
The way airplanes create lift is by using wings. If we 'fix' the wing for simplicity (that is, forget about flaps and other devices that change the wing1), there will be only two variables under the pilot's control that effect lift:
- Angle of attack (AoA).
- Airspeed. (Pilots usually talk about indicated (or calibrated) airspeed rather than true airspeed. It implicitly includes air density and thus altitude).
The more of each, the more lift. The dependency is quadratic on airspeed (double airspeed, 4x the lift), and more or less linear on AoA (until you get closer to stall).
What determines stall is, in practice, solely the AoA,2 as you already understand. If you had an accurate AoA sensor, that's all you'd need to watch in order to avoid stall. (But you'd still need to have knowledge of how the airplane flies, i.e. the above dependencies, in order to know what to do to avoid it).
However, for various reasons you usually don't have such sensor. In this case you can use airspeed as a proxy. But airspeed is linked to AoA via lift, as we discussed. You need to know the current lift, too! How do you know it? Well, in a straight and level flight, lift exactly equals weight, by definition. You know your weight because you filled in the weight & balance chart prior to flight, right? You also know how much fuel you used up to this point.
So, the heavier your given airplane is (say, if you load an extra passenger), the more lift you'll need in the same conditions. And as we know, we can create this extra lift in two ways: by increasing AoA or by increasing airspeed, or both. If we just increase AoA, we'll obviously get closer to stall, and at some point we'll stall - at the same airspeed as we were perfectly able to fly with lower weight. Or, the other way round, if we 'fix' AoA (say, consider the stall AoA - which is fixed, as we know), we'll need higher airspeed for higher weight. (1.4x airspeed for double weight).
This is why your stall speed varies with weight. It also varies with G-loading, which is the case when the wing needs to create more lift than weight. (Coordinated turn is the first manoeuvre that pilots learn when this happens). When the documents (such as POH) specify 'stall speed', they also specify the weight at which it applies. (If they don't, they conservatively imply maximum permitted weight). They also often have charts how the stall airspeed increases in turns (as a function of the bank angle).
So, when we talk about 'stall airspeed', we understand it as 'airspeed at which the wing produces the required amount of lift while being at the stall AoA'. The 'required amount', in turn, depends on the conditions being considered: for the simplest case of straight and level flight, this is just the weight.
1 As well as about ice, bugs and dirt on the surface, etc.
2 In truth, true airspeed also has an effect via Reynolds number (Re), but in the context of GA this effect is very minor. The rate of change of AoA also matters, but only for very aggressive manoeuvres, like in aerobatics.