Within the European Union, you don't invoice VAT when the invoice is outside your own country to another European country (my last invoice was from Belgium to Portugal: 0% VAT). But, in the monthly or three-monthly tax and VAT declaration you have to inform tax authorities about these invoices.
When I make an invoice to a Belgian company, I invoice it with 21% % VAT, and I can get it back: it is is a balance between incoming and outgoing invoices. When your business is healthy you usually have more outgoing invoices than incoming invoices.
My explanation isn't that of an accountant, it is my engineers explanation, I don't understand the languages of accountants, as they don't understand my language
with due respect