Yes, you are correct.
The only difference between 3 phase and single phase is that there are 3 different, independent sources of power at the alternator.
The 3 phases are 120 degrees "away" from each other so that each one peaks at a different time during the rotation. The end result of this when combined and rectified to DC is a more constant power output, that is more efficient to transfer over the wiring that connects the load to the generator.
These phases are then usually wired together in a scheme that additionally reduces the number (or size) of conductors needed to carry the current away from the genny, although not always. The rectification can take place anywhere from right at the turbine, to right at the batteries, or somewhere in between. Sometimes it is desirable to take 6 thinner wires down the mast, rather than 2, 3, or 4 heavier gauge lines (depending on the topology of the coil connections, and where rectification takes place). It all depends on the intent of the design; the turbine's power output capabilities, the length of the run from turbine to battery, and so on.
Either way, there are typically only 3 ways that a 3 phase alternator's output is configured, before being changed into DC. They are:
Delta - Gets it's name from the shape of the greek letter it's named after. The 3 sets of coils are wired end to end in a triangle, with each of the 3 power taps taken from the points on the triangle. This is then fed (in this case) to a special 3 phase bridge rectifier composed of 6 diodes, 2 for each phase. The DC from these rectifiers is then combined to form a single, two conductor output that connects to the load (batteries).
Wye - The inverse of delta, once again named after the shape they take on a schematic, the coils are wired so that one end of each coil terminates at an output, with the other end terminating at a common point. This wiring scheme has 4 conductors carrying the power away from the genny, and are also connected to a special bridge rectifier designed for 3 phase use. There are a couple of ways to conjure the DC from the bridge at this point, but in the end, the result is the same - the final output is two conductors, one positive, one negative, heading for the load.
IRP - This stands for "Individually Rectified Phases", and means that each coil is completely independent on the AC side of the bridges, and they are each fed to a standard bridge rectifier (of the 4 diode variety), then the DC sides of each bridge are tied together to give (you guessed it!) a single pair of positive and negative, headed for the load.
There are reasons to go with each, as they all have pros and cons, some provide higher voltage while trading off current, some provide higher voltage at lower RPM, higher current at a lower voltage, etc etc...
The design of the windmill plays into this, as well as the typical wind conditions for the area it's erected in. EDIT - There are even schemes to change between these methods on the fly depending on what the most efficient way is for that particular moment...
The nominal voltage of the system does not really have anything to do with how the phases are wired; the concepts are the same for any voltage range. The effects of using one method over another for arranging the coils electrically and how they are rectified is more about the turbine and it's associated wiring, not the batteries. These differences are also relatively subtle; the voltage range does not change significantly enough to switch between different nominal system voltages for example, but more to compensate/tweak for cut-in and the like.
Nominal voltage of the entire system is determined by several factors, but usually the most significant is cost vs. need. The inverter you intend to use with the system typically determines what you need the nominal voltage to be, then the batteries selected and wired for that range, and then the turbine's properties, and so on.
Hope that helps a bit...
Steve