A subpoena is a demand to appear issued by a lawyer. A witness has to be subpoenaed to something. You subpoena testimony, usually by deposition, to a hearing or to a grand jury. A subpoena duces tecum is a subpoena to show up and testify and bring documents, too.
Government subpoenas are usually in connection with civil enforcement. In the criminal context, they are to compel a witness to a grand jury or to testify at a pretrial deposition or at trial after the suspect as been charged, or in the case of secret proceedings, when a grand jury has convened.