I'll share the Spanish situation:
After passing your exam and paying a fee, you obtain an Authorization with your call sign, this allows you to operate in the ham bands, and is all that is required for portable and mobile operation. It is nowadays (usually) a digitally signed PDF available in two versions: the "classic" one and the "card" format.
Then there is the amateur station licence, which is required to install and operate a fixed station, and is concerned with the legality of your antenna and transmission lines, intereference, and civil engineering concerns (such as wind loads and other stuff about which I know nothing).
If you move or change your personal details, you send an electronic request to the local Telecommunications authority and they send you a new PDF with the data amended. Since the PDFs are digitally signed, one can verify they're genuine by checking them in an official website or checking the validity of the signature in Adobe Reader.
73 de EA4FYQ