The Steuer-ID is sent to you by post a few weeks after your Anmeldung. It stays the same for your whole life, even if you move or leave Germany and come back later.
Your employer needs it to apply the right tax class, and banks need it for withholding tax on investment income. It is not the same as the Steuernummer, which belongs to a specific tax office and case.
Full guideTax ID, tax number, VAT number: which is whichRelated terms
General information on German tax law, not advice on your individual case.