There are enough differences between wind and solar, so a system design is important, not just a choice of inverter.
I always feel bad doing this but to nitpick on some stuff, a "controller" is used to regulate a wind turbine output, and an "inverter" delivers AC from a DC source. Some Solar Inverters can go without batteries, and connect between solar panels and grid and handle all the stuff that's happens there. Not so common to do that with wind - usually you use a controller and a set of batteries. Bigger scale stuff doesn't need the batteries, but then it's a grid-tie at a commercial scale, and the turbine has to support doing that just like the inverter.
A charge controller that can handle a wind turbine can, as Damon said, absorb transients on the power supply, and it's designed to keep the load on at all times. If it's a MPPT wind controller, then it goes between the turbine and the batteries, managing the turbine operation. If it's not a MPPT, then the charge controller just manages a diversion load so that the batteries don't over-charge. This stuff doesn't matter in solar, so an inverter designed for solar is much simpler. As you noticed, there's also a possible 3-phase supply or a DC supply in wind, and solar is always just DC. That said, the solar grid-tie inverters can have a lot of features that the wind controller can't.
Best way to learn about it (IMO) is to keep reading those installation and operation manuals.