Social security card: If you want to work in Germany, you need a Sozialversicherungsausweis (social security card) with a Sozialversicherungsnummer (social security number).
Your health insurance company, the BfA (Federal Employment Agency) or your employer will register you with the German pension scheme. You will then receive your insurance number. Please inform the relevant people if you already have a German insurance number.
Tax number: You also need a Steuernummer (tax number). After you have registered, the Bürgerbüro (citizens’ office) will automatically transmit this data to the Finanzamt (tax office). You will then receive your tax number from the tax office by post.