The first thing is that these expressions begin one part of a two-part sentence. The other part is something that contrasts against or contradicts the part with these words. Use "although / though / even though" plus a statement. "Even though he hadn't studied, he still passed the exam." Use "despite / in spite of" plus a noun or verb in gerund form. "We enjoyed the holiday in spite of the weather." "Despite not having studied, he still passed the exam."

Me hablé a mi por unos minutos con las frases mencionadas arriba, y sí, creyo que tu observación es correcta. Unas cosas: -Frequentamente, "despite/in spite of" va con "the fact," especialmente "in spite of." Por ejemplo, "The store is open in spite of the fact that today is a holiday." Las otras palabras--although, though, even though--no usan esta construcción. "The store is open even though today is a holiday." -"Even though" parece más a "despite/in spite of" en este caso y otros también. Nunca diría "The store is open (although/though) today is a holiday."