A spell is any kind of intention cast out into the universe with willpower and/or supernatural power behind it. It’s a desire that is deliberately made manifest. Enchantments, charms, hexes, jinxes, and curses are all spells.
A jinx, hex, and curse are all different degrees of baneful magic. A jinx is basically bad luck. It’s annoying and may screw up something important, but it’s not life-ending. A hex is worse. A hex makes your milk turn sour, your family and animals get sick, your crops die, etc. A hex does a number on you. A curse is really bad. It causes devastating harm, or lasts for a really long time and is harder to get rid of. It may even last for multiple generations. A curse is on the level of a divine punishment, and in most cases, casting one is evil.
An enchantment is a spell placed on something — a person, an object, a place. If something is “bewitched,” then it’s enchanted. “Charm” can mean the same thing as “enchantment,” a spell placed upon something, but it can also be a word for the enchanted object itself. It could be considered a general term for amulets and talismans.