These two adjectives, though related, have quite different meanings.
Official means “recognized by or representing an authority, such as a government.” For example, official documents, official identification, official permission, etc.
Official can also be used as a noun to refer to an official representative of authority:
The official at the border asked to see our official documents.
Officious describes the behavior of people who represent authorities or bureaucracies—behavior such as worrying too much about paperwork and procedures:
The officious behavior of public servants can be frustrating to people who need help.
Citizens often worry about the officious behavior of their government intruding into their private lives.