Can someone explain to me why when its CO2 that's causing problems in the atmosphere people keep referring to carbon?

Its leaving me more and more confused - when they're talking for example about carbon trading, reduced carbon footprint or lower carbon emissions do they mean CO2 ?
It grates on me everytime its used because I don't know what they mean - is it lazy media speak Or is the carbon / carbondioxide thing inextricably linked? As in where there's carbon there's carbon dioxide? As in if you use less carbon based fuel then there's less CO2 released into the environment?