Apostille refers to a certification authorized under Convention 12 of the Hague which allows a government office (for example, the Texas Secretary of State) to recognize a document for use in a foreign country without certification from either the US State Department or the country’s embassy or consulate. This option is only available to countries which are part of the Hague Convention.
Authentication is the process by which the US State Department certifies the signature or seal of another US government agency (for example, the Delaware Secretary of State) on a document for use in a foreign country.
Legalization is the certification of the signature or seal of a US government agency by a foreign embassy or consulate on a document for use in a foreign country.