DTS is not an acronym for Deville Touring Sedan on '06+ cars. The last Deville is a 2005 model.
Pre '06, DTS was a trim level.
'06+, DTS is a model.
They're both "real", but a pre '06 DTS was the top of the line/performance oriented Deville. After that, it could be the top of the line performance model, or a base model. It lost its "special" meaning, so some poke fun at that fact.