In vehicles, there is a difference between generators and alternators.
First, what is shown in the photo, is not a (DC) "generator" rather it is an AC alternator which includes a diode bridge (3 phase, 6 diodes) to rectify into DC.
Let's make sure you understand this first.
Originally generators were used with commutating windings with brushes making contact with rotor windings to alternate the AC voltage back to DC.
Due to brush arccing failures in the late 60's these were redesigned with Alternators that use copper slip rings to provide DC to the rotor instead, which we call self-excited since it can use the rectified output voltage to excite the rotor current so that the rotating flux can effectly increase the output AC current amplified by the work done to rotate the pulley and regulated by the output voltage to 14.2V with a regulator that has a fixed low voltage reference.
Next we know that motors/generators and alternators produce a "no load" EMF voltage proportional to RPM, but in this case the regulator controls the rotor (rotating DC) "Field current" to also regulate voltage as RPM changes. However below a certain RPM, no amount of field current can raise the voltage, this only gives current gain.
So RPM creates the voltage while field current automatically regulates the output current determined by the internal voltage regulator and load current (Ohms Law, Vout= Iout(load)*R(load)). So the field current naturally reduces with rising RPM at a fixed load.
However we know that the load also affects voltage by impedance ratio, so the source impedance must be lower than all expected loads except for the starter motor, which is a much lower impedance but like a generator it has a commutator with heavy copper brushes.
So the Alternator produces both voltage and current regulated by RPM and field current, so we say it generates power that depends on load. Since the available torque is high from a serpentine belt, it may be undervoltage below 500 RPM but be able supply full power at 1200 RPM or so using engine RPM scaled to alternator RPM by pulley ratios.
In short (no pun intended as that would blow the 6 diode bridge at high RPM) the alternator is a voltage regulated current controlled current source at fixed RPM that supplies all the current needed to charge the battery and other loads. It must be suitably sized for current as the battery ESR determines the max current to raise the voltage to 14.2V and the battery ESR reduces with rising CCA capacity (when new) needed to turn a big truck starter motor.
side effects from mismatched alternator and battery
Although a vehicle, once running can operate without a battery, the alternator must have the current capacity at correct regulated voltage voltage and current to meet expected demands. The biggest load is a an undercharged battery. When batteries age each cell becomes more mismatched and the weakest cell can boil the electrolyte from over voltage from excess alternator current to reach 14.2V so instead of 14.2/6=2.366V per cell, anything 10% higher will age the battery rapdly. So installing a bigger alternator on an old battery, can result in battery failure quicker than normal. Also as diode bridges get hotter and age slightly with higher ESR a fresh battery with higher CCA rating (and lower ESR result) can increase the stress on the alternator bridge and fry it in ar least one phase so the alternator reduces its capacity from 3 phase to 2 or 1 phase and can no longer keep up to worst case load current causing the headlamps to dim at normal idle.
Lets consider a new 1000 Amp CCA rated battery that when warm has CA rating of 1200A. This means the ESR is (12.5v-7.5V)/1000A= 5 mΩ from the std test at drop to 7.5V and Ohm's Law. So what is the max current to raise the battery from 12 V (undercharged) to 14.2V ? Again from Ohm's Law, (14.2-12)V/5mΩ= 440 amps !! Fortunately the diodes can handle brief over current periods and the weak alternator could fry its diodes , while a stronger one might need more RPM to raise the voltage to 14.2 until the charge level rises.
Thus the alternator current and battery CCA are designed for each vehicle to increase longevity at the least cost by careful selection of matching diode ESR and battery cell ESR mismatch from aging. This is why they sometimes dont last long after replacing one or the other. This is aggrevated by excessive V regulator settings and poorly sized or maintained batteries. (warped plates from brief shorts), excess ambient temperature baking in the sun in Arizona. etc etc.
Sorry for the long answer, I hope this raised your IQ on Alternators. It is more complicated as the control loop is a current controlled current source (CCCS) with a Voltage Reference to get an output of 14.2V +/-0.1. This results in it becoming a regulated Voltage source. The other answers at this time, do not mention this at all.