Yeah, there are basically three differences between exertions and wounds:
1. Exertions and wounds are different terms, so if a card affects exertions it doesn't affect wounds, and vice-versa.
2. You take wounds from the enemy archery total, losing skirmishes, and threats (in contrast, the only way you ever get exertions is from the game text of cards).
3. Exhausted characters (characters with one vitality) can never exert, but they can take a wound (which will kill them unless a card prevents it).