tribunal de primera instancia; tribunal competente en primera instancia; tribunal competente en (primera y) única instancia; tribunal de última instancia; juzgado de primera instancia

These expressions are indeed confusingly similar, but are definitely not interchangeable. Tribunal de primera instancia is a general term for any court of first instance and can probably be best rendered in English simply as “trial court.” In contrast, tribunal competente en primera instancia denotes a “court of original jurisdiction,” i.e., a “court where an action is initiated and first heard” (Black’s Law Dictionary), which is not necessarily a first instance or trial court. Thus, competencia en primera instancia is “original jurisdiction.” As an example, in the event that a deputy or senator (diputado o senador) of the Spanish Parliament (Cortes Generales) were accused of a criminal offense, he would not be tried by a criminal first instance (or) trial court, but rather would have the privilege (called aforamiento) of being tried by the Criminal Division of the Supreme Court (Sala Segunda, de lo Penal, del Tribunal Supremo). Indeed, the Supreme Court is the “court of original jurisdiction” (tribunal competente en primera instancia) for trying Spanish deputies and senators for criminal offenses, or expressed otherwise, the Supreme Court has “original jurisdiction” (competencia en primera instancia) to hear criminal cases against deputies and senators.

If a court is described as competente en primera y única instancia (or simply en única instancia), it is a “court of first and last resort,” having original jurisdiction to first hear a case, but whose decisions are not subject to appeal. Tribunal de última instancia is a “court of last restort,” a court that hears the final appeal of a case. And, finally, in Spain juzgado de primera instancia is a specific type of court, being the first instance court for civil proceedings. In that regard, juzgado de primera instancia may be appropriately translated simply as “civil trial court.”