Launch Leagues: Long-term injuries are disabled. During a Launch League game, if a player gets injured, he will be ready for the next game, unless he is injured as a result of overuse or tiredness.
Those situations result in day-day injuries which are NOT turned off in Launch Leagues.

Disabled Lists: PureBaseball leagues do not maintain disabled lists. If a player is injured, he can be moved to the non-active roster (farm team).

Day to Day Injuries: Injuries which are caused by overuse or tiredness. The length of injuries is affected by the severity of the tiredness or overuse. These injuries are enforced and present in Launch leagues as well as perpetual leagues.
This type of injury occurs when a player is used in a game while overused or tired.
This can occur if player appears in a game with one of the following status'; Overused, Very Overused, Tired, or Very Tired.
Additionally, a Day to Day injury occur if a Pitcher becomes tired during the course of the game. This occurs when he exceeds his BFA and the text in the game identifies him as tired.
Injuries of this type (Day to Day) are generally of a short term, but their duration can be longer if the player is extremely overused or tired. Day to Day injuries can happen to ANY player regardless of whether or not they were hurt in real life.

Injury Number: A number representing the number of games missed by a player due to serious injury in the corresponding MLB season. A serious injury is defined as one which requires use of the disabled list.

Long Term Injuries (serious injury): Injuries which are triggered by the game action. Players with a "0" as their injury number can't be injured except for the rest of the game in which they are hurt.
Long Term injuries only occur to players who were injured (They had to have been placed on the DL for the injury) in the corresponding MLB season.

There are Two (2) important factors in deciding the duration of a serious injury. The First is "occurrences" or how many time that player was hurt in real life. The second is the total amount of games missed due to injury.
PB uses these two factors to decide the injury.

Each time a player is hurt, PB injures him between 25-75 percent of his real life injury duration.
Example: In 1997 Reggie Sanders was hurt 4 times for a total of 81 games for an average of 20 games per injury. This means that Reggie Sanders can get a serious injury up 4 times in a season. (Once for each occurrence.) When he gets hurt, the injury will be between 5 (25% of 20) and 15(75% of 20) games.

SPECIAL NOTE: A player who has used all of his occurrences can still get hurt. If you have a player who was injured during the corresponding MLB season, he will never be completely safe unless he has reached his total games injured total. If he does get hurt, he will be susceptible to a Day to Day injury, regardless of whether or not he was overused. Players will never, however exceed there real life injury totals.
Day to Day injuries due to overuse (Day to Day injuries) DO NOT count toward a players injury day total.
All other injuries do (Day to Day injuries to players who were injured in MLB but whose injury number has been reduced to "0").

Injury Page: There is a link on the Stats/Roster page (From Team Page) to a page which keeps track of your players' injuries. That page will have all the information you need to keep track of your player's injuries and injury occurrences.
You will also want to check that page if you are trading for a player who was injured in the corresponding season.