-Remodeling is replacing existing fixtures/floors/cabinetry etc.
-Rebuilding (to me) means "gut-renovating", gutting down to the studs so the work includes new electrical wiring, new insulation, new pipes, but the original structure is used.
-New construction is when a brand new home is built on land - or after the existing structure was torn down. Even the studs are new. Sometimes the owner/builder leaves the existing foundation but the entire structure above ground is brand new, and I still call that 'New Construction'.