wound is commonly expected to involve a disturbance of some kind to the skin: a laceration, puncture, burn/blister, avulsion, etc. (The given definition is an injury, especially one in which the skin or another external surface is torn, pierced, cut, or otherwise broken.) A small wound can heal in 5-7 days; a deeper wound in a few weeks. Even horrible wounds (with care) can be seen to heal in time, often even day by day.
I think the key is in seeing.
Many injuries (damage or harm done to or suffered by a person or thing) do not visibly "heal", and those that do certainly take much longer than wound healing. For example, a broken toe is certainly an injury. It takes about 6 weeks to heal well enough to stop causing pain, 8-9 to heal completely (depending on use). A ruptured spleen is a serious injury, but you can't watch it heal without specific imaging tests. Same for head injuries, muscle/kidney/joint/ligamentous/cardiac (yes, you can injure your heart)/liver/etc.
Injuries often do heal. People just tend to refer to that process as getting better, not healing.
Googling the wound heal will give you hits about visible wounds.
Reducing the bacteria levels helps the wound heal faster.
Googling the injury heal will give you half as many hits, mostly about joint/muscle/head injuries, etc.
If you have pain along the shins during activity, stop immediately and let the injury heal.