The decoy matches are certain to be spurious identifications, but we can't discriminate between true and false positives identified in the target database. FDR estimation was added in response to journals' guidelines on protein identification reports like the ones from Molecular and Cellular Proteomics. Mascot's FDR calculation incorporates ideas from different publications.
False positives are undoubtedly incorrect identifications, but we cannot distinguish between actual and false alarms within the target database. The incorporation of FDR estimation was a response to journal guidelines for protein identification reports, similar to those found in Molecular and Cellular Proteomics. Mascot's FDR calculation builds upon concepts from various academic publications.