"Hurt" can be emotional, figurative, or physical, "injured" can only by physical. "He hurt my feelings."The bad weather hurts our chances of survival" Those are instances where "injured" cannot be used. When talking about a car crash, injured is better. Hurt is usually used about less serious injuries.

Hurt has a wider, more general meaning. Injured is usually more specific. In your example, I would choose 'injured' because it is very naturally paired with 'seriously' when describing physical damage to a persons body in an accident. 'hurt' can also refer to physical damage, but it can be used for other types of pain, like emotional hurt or mental trauma too. Although I have heard 'mental injury', the word injury most naturally implies physical wounds on the body.

It depends on what to use but you can use them in a similar way or interchangeably. Example: I was hurt from the fall with a bruise on my leg. Meaning a light injury. I was injured in a car accident so I can't walk. Bigger impact of an injury.