The TAX ID and VAT ID serve different purposes.
The VAT ID is a proof that the company is registered for VAT and identifies the company for VAT related transactions, usually, it’s in the form GB 12345678, where GB is the country 2 letter ISO code. You can read more about this here.
The TAX ID identifies the company to the inland revenue, which is separate from VAT related transactions.
Even if in some countries they are practically the same numbers, keep in mind that they serve different purposes.
The VAT ID and TAX ID of a new country will be automatically added after the registration. If you want to add a new VAT ID or TAX ID go to the VAT Calculation menu and click on either the country where you want to add the VAT ID/TAX ID or on add new country if the country is not in the menu yet.
In the menu, you just opened, enter the VAT ID and/or TAX ID like in the example below and click the save button.