Sample sentences: - Police say one gunman was killed, and other is in custody, seventeen other people were shot and wounded. Five people suffered non-gun-shot injuries.

Then one hour later it reported again:

One of two gunmen is dead. The other is in custody. Authorities say a total of 17 people suffered gun-shot wounds.

If you break your leg, you are injured but not wounded. Many injuries of that type occur, and would not be referred to as wounds.

In general terms, any type of bodily harm can be described as an injury and if bleeding is involved the bodily harm is also a wound. Bodily harm that involves trauma to the brain or a broken bone, for instance, is not a wound. But it is an injury.

Conclusion: A wound is an injury. An injury is bodily harm. But not all bodily harm is a wound. There are all types of bodily harm (trauma, internal injuries, etc.) that do not involve piercing or opening of the skin with bleeding on the outside. We say internal injuries, and not: internal wounds.

The semantic trait difference between wound and injury is that a wound involves "piercing, cutting or breaking of the skin" whereas injury does not specifically involve that. (the metaphoric meaning of wound here is not addressed per se.)