Flight 588 SEA-MSP is a continuation of flight 588 PVG-SEA. While sharing the same flight number, the flights are flown on different equipment (PVG-SEA is an A330-200). Flight 588 SEA-MSP is flown on a domestic 763 with standard domestic FC seats. Your ticket carries a "Business" designation only due to the flight sharing the same flight number with PVG-SEA and it does not actually indicate any particular level of BE seating or service. This has been a much discussed issue of confusion here on FT.