Five years after the Satanic Temple of the United States made headlines — and unleashed a wave of panic — when it was designated a church, a similar organization in Chile, a conservative country where half of its population of 18 million identifies as Catholic, is asking the government to recognize them legally as a religious association.
According to the article this is a similar organization, not The Satanic Temple.
Not necessarily all the time. The Satanic Temple in Spanish is El templo satánico where the Temple of Satan is El templo de satanás. one is an adjective and one is a pronoun and noun