There are in fact at least three (I say that because I know of 3, and there could be more) different methods used. So to say “all aircraft” is not quite right. Lets start with what I think is the single most important equation, Faraday’s Law (simplified):
$$ \mathcal{E}=-N\frac{\mathrm{d}{BAcos{\omega t}}}{\mathrm{d}t}\ $$
This tells us there are a number of ways to produce a given output EMF ($ \mathcal{E} $). The two that are relevant for this discussion are B and $ \omega $. Note $ \omega $ is the angular frequency, which can be scaled to RPM.
GA aircraft, including biz jets, will likely be using a DC generator or a DC alternator. In a DC system, given these are small light aircraft, we actually control B in Faraday’s Law. That is, if the RPM increases, then we reduce the magnetic field strength inside the generator. This results in a balanced output. The generator control unit (GCU) is responsible for doing this. Effectively, it is continuously measuring the output of the generator (or DC alternator) and as the output voltage falls, the current provided to the field windings (the coils or wire that produce the magnetic field, which is an electromagnet) is increased. Similarly, if the output goes high, the current to the field windings is decreased. The circuit is shown below [1].

For large transport category aircraft, there are two options. These are the legacy systems (as answered by others) and the modern more electric aircraft solution, used in the B787 and the A350 (and I am sure on modern variants of older airframes). As previously mentioned, for legacy large transport category aircraft, the part of Faraday’s law that is controlled is the RPM. This cannot be done inside the AC alternator, so it needs to be done before it. As mentioned, the constant speed drive unit (CDU) is combined with the AC alternator to give an integrated drive generator (IDG). The CDU is a hydrostatic transmission system. In this, the input rotation pumps a hydraulic fluid, which depending on the input RPM will increase and decrease in pressure. The GCU now actuates a wobble plate in the transmission systems which ensures the output hydraulic fluid pressure is constant. This constant pressure fluid is then given to the output “turbine” or hydraulic drive, which rotates the output at a constant rate. This gives a constant RPM for the alternator. A figure is show below, although not super helpful [1].

For modern large transport aircraft, none of the above happens. These are called ACFW systems, that is AC (alternative current) frequency wild systems. Here, we let the starter generator (which still does have a GCU, so there is an operating band that needs to be maintained) rotation change with the RPM change of the engine. This generates wildly different AC frequencies at different times (engine RPMs). This is then immediately converted into DC. For this to be utilised in systems that require AC current, the typically 3 phase 115V/120V 400Hz signal, then static inverters are used to convert the DC signal into the require AC signal. In these, we effectively switch on and off a DC signal, give it to a transformer (and other conditioning circuitry) to make the required AC signal. The same kind of power system is utilised in the F-22 and F-35, for example.
References:
[1] FAA. (2018). Aviation Maintenance Technician Handbook - Airframe Volume 1. Federal Aviation Administration. PDF (194 MB)