Those cars, regal, century and Grand prix 1997-2003 were all built on the same platform. The W-body. Meaning everything on the underside of those cars is exactly the same. Granted the different trim levels and bigger engines and such. They are are the same.
The interiors are not the same however. To grab a carpet from a century and put into a regal. Yeah it will work. Those two cars are the same. The Regals were just a bit more sporty and over the century but it'* the same car. Now the grand prix is slightly different from those two cars. I bet a carpet from a Grand prix 97-03 could be made to work in a Regal or century.