What is the physically unable to perform (PUP) list and how does it work?
The physically unable to perform list, better known as PUP, is a designation for players who are physically unable to perform football services due to football-related injuries. These players can participate in team activities but are not allowed to practice.

[list]Active/PUP list: Players are placed on this list during training camp and count toward a team's 90-man roster. Players can be removed from the list at any time during camp, but can't be placed back on the list. Players on this list as of final roster cutdowns must be placed on the Reserve/PUP, released, traded or counted against the 53-man roster.

Reserve/PUP list: Teams must decide by the 53-man roster cutdown deadline (Aug. 30 this season) whether to place a player on this list. Players placed on this list at that time must miss at least the team's first four games -- down from six in seasons prior to 2022. Unlike in the past, players can be activated immediately after such time has elapsed. Any player who is designated Reserve/PUP on or after rosters are reduced to 80 (Aug. 23 this season) will also be subject to the same four-game absence.

Players on the PUP list are paid their entire base salary. A player's contract will not be tolled (meaning the contract will not be suspended and resumed the following season) while on the PUP, unless he is in the last year of his deal and he is both not able to perform football services as of the sixth regular season game and is not activated during that regular season or postseason.[/list]

What's the non-football-injury (NFI) list and how does it work?
The Non-Football Injury or Illness list (NFI) is similar to the PUP list, but it is used for players who suffered injuries or ailments outside of NFL activities. This can range from Minkah Fitzpatrick's wrist injury falling off a bike on vacation to Jameson Williams and John Metchie III's ACL injuries in college. Players who begin the season on NFI (as of cutdowns to 53-man rosters) can be activated after the team has played its first four regular season games.

However, a player on this list is not entitled to receive his salary, and his contract will continue to run while in such status. That said, the team and player can negotiate a rate of payment for the player while on this list.

If such a player is in the last year of his contract (including option years), his contract will toll, provided the player is not physically able to provide his services by the team's sixth regular-season game and the team pays his prorated base salary for the balance of the season after that date. If the player is taken off of NFI during the league-allotted window, his contract will not toll.

What is injured reserve?
The Reserve/Injured List, better known as injured reserve or IR, is a list for players who have suffered a football injury that makes them not immediately available to their team. When a player is on injured reserve, he is not eligible to play for his team. There's no limit to the number of players who can be placed on the list, but there is a cap on those "designated to return" from the list. Players placed on injured reserve prior to the close of the waiver period following final roster cutdowns are ineligible to return that season.

Per NFL Network Insider Mike Garafolo, the NFL and NFLPA agreed to amended IR rules during the 2022 offseason. Each team can now designate up to eight players to return from the Reserve/Injured or Non-Football Injury/Illness List. Each player may be designated to return twice in one season. However, both designations will tally toward the limit of eight. Players must remain on this list for at least four games prior to returning to the active roster. Teams can begin to designate players to return on August 31 this season.

Here is a list of other notable reserve designations for NFL players:
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Reserve/Suspended: Any player who is currently suspended from the NFL. Such a player does not count toward roster limits and is not paid his base salary while on this list. Atlanta Falcons WR Calvin Ridley is a current example of someone on this list.

Reserve/Retired: Players who have filed retirement papers but are under contract with the team. This player's salary counts against the cap as if he had been released. Any future bonus prorations will accelerate onto the salary cap. The Tampa Bay Buccaneers were charged more than $7 million in signing bonus prorations after Ali Marpet's retirement this offseason.

Reserve/Did Not Report (left team): Players who have left their team or stopped playing NFL football but have yet to submit retirement papers. This player does not count against a team's roster limit or its salary cap. This offseason, the Baltimore Ravens placed undrafted rookie receiver Devon Williams on this list when he did not show up for training camp. Williams was reinstated days later before ultimately being released.

Reserve/Military: This list is for players who have to complete military service while signed to an NFL contract. Such a player's contract is tolled, and he is not paid, nor does he count against roster limits. The latter is true until he plays in his first game.

Reserve/Commissioner Exempt List: This list is for players in special or unusual circumstances who are momentarily not counted against a team's roster limit. The Commissioner is the only person or entity who can place a player on this list.[/list]

https://www.nfl.com/news/nfl-training-camp-roster-faqs-defining-injured-reserve-pup-list-nfi-and-more 

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