That's likely coming from different reporters talking about things from different angles. A shrinking population is a potentially big economic issue it puts stress on all sorts of things chiefly the Social Security system in the US (and those like it in other countries).

Ultimately I don't think we'll be able to population shrink our way out of climate change, at least not on timescales and in ways that people are willing to accept. It's just coming too fast and the population changes so slight that it's not going to come in as a last minute solution.