banish implies compulsory removal from a country not necessarily one's own.
banished for seditious activities
exile may imply compulsory removal or an enforced or voluntary absence from one's own country.
a writer who exiled himself for political reasons
deport implies sending out of the country an alien who has illegally entered or whose presence is judged inimical to the public welfare.
illegal aliens will be deported
transport implies sending a convicted criminal to an overseas penal colony.
a convict who was transported to Australia
Example Sentences
He was banished for life. The dictator banished anyone who opposed him.
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Word History
Etymology
Middle English banysshen "to condemn by proclamation to leave a country, exile, outlaw, expel, drive away," borrowed from Anglo-French baniss-, stem of banir "to proclaim, (of a king or noble) summon by a call to arms, condemn by proclamation to leave a country, exclude" (also continental Old French), going back to a Gallo-Romance adaptation of Old Low Franconian *bannjan, verbal derivative of *banna- "summon to arms by a lord" — more at ban entry 2
Note: Compare Medieval Latin bannīre, bandīre "to summon by public authority and compel performance of something" (this sense is already in the seventh-century Lex Ripuaria, the laws of the Ripuarian Franks), "to require by public authority, place under a prohibition, excommunicate." Compare also bandit.