This was intended as a comment to Joonas' answer, but it was too long and somewhat different.
I'll explain it using my native Czech, which has both variants, similar to Latin and English fear sentence structure. These are synonyms: "Bojím se, že přijde." (lit. "I fear that he comes/will come.") = "Bojím se, aby nepřišel." (lit. "I fear so that he won't come.", or "I fear, so I wish he won't come."). They can't be used both as synonyms in a sentence expressing positive emotion, but both structures are used for different, similar verbs. In the "English" structure: "Doufám, že přijde." ("I hope he will come.") or in the "Latin" one: "Chci, aby přišel." (lit. "I want that he comes/will come", or "I want him to come").
Czech "aby" corresponds to Latin "ut" and English "so that" and "aby ne" (the negation "ne" is usually used as a verb's prefix in Czech: "nepřišel") to Latin "ne" and English "so that" + negation. So:
Czech "Bojím se, aby nepřišel." = Latin "Timeo, ne veniat." = literal
English "I fear so that he won't come." = natural English "I fear he
Czech "Chci, aby nepřišel." = Latin "Spero, ut veniat." = English "I
hope he comes."
Sometimes I feel sorry about you poor native English speakers. So many things in other lanuages are easy and logical, but your language complicates it all by devolving too much from Latin where other European languages keep stay closer to the Latin original.