I know both of them means Climate change but I want to know when either of them is used.
Klimaänderung describes a specific change (eg. temperature) or a few things that change which could also happen in a sauna.
Klimawandel means the thing that is happening to our world.
The word used usually in German is "Klimawandel". While "Klimaänderung" transports the same meaning "Klimawandel" simply is the established term.