Sew foam is softer open cell polyurethane foam with a backer fabric bonded to it that will hold a stitch line. The closed cell foam you are looking for goes by the brand name Volara. It is very firm and is used to sculpt shapes for door panels, etc. CLICK HERE
The Sintra or Komatex PVC foam board is rigid and is used for making door panels, etc. The Volara would be glued to the Sintra.
Airex is a type of PVC foamboard. It is generally used in marine construction in greater thicknesses like 1" or more sandwiched between fiberglass layers as a core to create lighter weight structures like hulls.
PVC foamboard is very versatile. It can be cut and shaped with ordinary woodworking tools, it can be heat formed, and can be glued together with gel type super glues.