This doesn't affect your inverter at all but there are normally differences between solar and wind controllers.
Wind generators need to be connected permanently to a load. The normal procedure is to connect directly to the battery and use a diversion controller to dump excess power to a dump load once the battery reaches the set voltage.
This method works perfectly well for solar, but with solar you can work in a different mode. As the panel voltages are limited you can just switch the panel on and off with a series pwm switch and that will regulate the charging voltage perfectly well and it saves the cost of a rather expensive dump resistor.
Most controllers can be connected for series pwm ( solar only) or for diversion for wind or wind and solar. Usually they can also be connected as a low voltage disconnect to protect batteries against excessive discharge.
They can only be used in one mode, you have to choose that to suit your charging source. If you need low volt disconnect then you need another device connected as a charge controller.
This doesn't affect your inverter in any way but you seem to have diagrams for an overall scheme. Inverters go direct to the battery ( usually they take too much current to via a low volt disconnect but that can be arranged if needed)
Probably best to download the manual for one of the Cx controllers then you will see how they can be connected to suit different needs.
Flux