Put simply, A shares are for Holland, (the old Royal Dutch Petroleum Company) - subject to Dutch withholding tax - and B for Britain (the old Shell Oil Company) - paid from "UK Sourced Income"
RDSA and RDSB are two different classes of shares for Royal Dutch Shell plc. RDSA shares are denominated in euros and have a Dutch source for tax purposes, while RDSB shares are denominated in pounds sterling and have a UK source for tax purposes. Both classes of shares represent ownership in the same company, but they have different legal structures and may have differences in voting rights or dividend payouts.
Shell is a subsidiary of Royal Dutch Shell plc. For Amsterdam and London, the ticker symbol is RDSA or RDSB. For New York, the ticker symbol is RDS.A or RDS.B.
On the New York Stock Exchange (NYSE) the symbols are RDS.A and RDS.B, on the London Stock Exchange (LSE) the symbols are RDSA and RDSB.