Personally I think a "new airport" implies a "new airfield" in a completely different location, ex. when Denver International Airport replaced Stapleton, that was a new airport. In ATL when the current midfield terminal opened, I don't think it was billed as a "new airport" but just a new terminal, and the old and new terminals had completely different footprints and no facilities or buildings in common.
Of course there are counter-arguments like the perpetually and embarrassingly delayed BER. It overlaps with the current SXF airfield and will even use some of SXF's runway and taxiways, but it's being billed as a "new airport." To make things really confusing, they're talking about keeping SXF open even though it was supposed to be shuttered. I don't how or why they'd be considered two different airports since they'll share an airfield. It should be two different terminals of the same airport, like the situation at BCN.
But to me SLC is just getting a new terminal building.