"collateral damage" is a very common phrase. Monica and Domasia both have very good answers on the definitions. I think any native English speaker would almost always use "collateral damage" in a sentence rather than "collective damage". It just sounds more natural. Hope that helps Matt

Collateral damage is something that happens as an indirect result. For example, other businesses collapsed, not because the mine collapsed, but because less people were in the area once the mine collapsed, and this negatively affected other businesses. The term 'collective' means 'as well as' or 'for the same reason.' The term 'collateral' fits better than 'collective' in this sentence because the economic damage was indirect, and from different causes than the mine closure.

'collateral' Meaning (to damage) not directly, but in the neighbourhood (/neighborhood), in the environment. Elements that are not linked directly. 'collective' would be second choice. But it does not fit so good. It could mean that some enterprises have a damage in property of common (/collective) ownership.