Unlike the Steuer-ID, the Steuernummer can change, for example when you move to an area covered by a different tax office. Freelancers and business owners receive one after registering their activity.
You put it on invoices if you do not have a VAT number, and you use it in all correspondence with the tax office.
Full guideHow to register as a freelancer in GermanyGeneral information on German tax law, not advice on your individual case.