verbs: to wound, to harm, to injure, to hurt
nouns: a wound, an injury (hurt and harm are more often used as uncountable nouns)
A wound is used for when you are cut, a flesh wound. Something received in battle. You can also be wounded emotionally.
An injury is more likely to be some sort of physical problem. Particularly from sports. The player was injured.
Hurt physically is more temporary. If I hit you you'll be hurt. You might receive an injury or a wound. Hurt is often used emotionally.
Harm is a bit more general. I hope you don't come to any harm.