Spells (or rituals) are feats of magic that are activated through an incantation, allowing the spellcaster to use magic to accomplish the desired effect. While most spells are required to be spoken, it has been shown that an experienced witch is able to perform a spell non-verbally or with merely a hand gesture.
Hexes and curses are dark spells that are used to cause negative effects to occur upon the target. A hex is generally an incantation which can affect the target for the caster's benefit or just for the target's detrement, generally to bring them bad luck or trouble. A curse is an encompassment of ill intentions which can cause harm to another person.