Waivers: A team has to cut players to get down to 53 man roster. The players that are cut are put on waivers. Any team can put in a waiver claim on any released player. If multiple teams put in a claim for the same player, the team that drafted higher gets the player. A player must pass through all teams unclaimed in order to be put on the releasing team's practice squad. All players that pass through waivers without being claimed are free agents and may sign with any team's practice squad or team. Only applies to players with less than 4 years of accrued seasons in the NFL. Players with 4 or more are considered vested veterans and are cut rather than waived. They are immediately free agents. Practice squad has its own rules of eligibility.
Injured Reserve: Injured players are put here when their injury prevents them from being able to play during the season. IR players do not count against the 53 man roster, but do count against the salary cap. No other team can claim or acquire players on IR. There is one designated slot for an IR player to be able to become active later in the season, all others are done for the season and may not return.
PUP: Physically unable to perform is where teams put guys when they have an injury that will not keep them out more than a few weeks. If a player begins the season on PUP, they can not return to the active roster until week 6 at the earliest. While on PUP, the player can not practice with the team. Between week 6 and week 10, the player MUST be added to the active roster or put on IR for the rest of the season. Players on PUP can not can not be claimed by or acquired by another team. To be eligable for regular season PUP, the player must NOT have practiced with the team since the beginning of training camp.