I admit that I do not completely understand all these terms, myself. This page is here to pass my knowledge, although possibly limited, on to you. All the information listed, I believe to be correct. If you know otherwise, then by all means, correct me.
Injured reserve is a reserve list that consists of injured players. A player placed on this list is ineligible to play or practice with the team for the length of the entire season. That player does not count towards a team's 53-man roster also, but players on this list also still cost money against the current year's cap. This list is best used for players that have little chance of returning before the season ends. A player can go on this list at any time during the regular or postseason. It is commonly referred to as IR.
Physically Unable to Perform is a reserve list that consists of injured players also. But this list allows that players still remain eligible for the current season. I don't know the exact dates, but typically a player on this list is inactive for up to 10 weeks of the season. At that point, the team has the option of three things:
Non-Football Injury list is virtually the same as the injured reserve. The only thing that differs is that the player's injury did not occur in an NFL practice. Players injured in NFL Europe are allowed to go on this list. Also plays that may suffer injuries or accidents off the field (e.g. car crash, assault, etc.) may go on this list. All the rules of the injured reserve apply here. But it might be possible that these players do not count against the cap. You may see it referred to as NFI.
Reserve Lists are lists that allow players to not count against the 53-man roster limit. The IR, PUP, and NFI are three examples of reserve lists, and the most common. Others that exist are the reserved/retired (for retirees), reserve/did not report (players who do not report to camp or practice), reserve/military, and reserve/suspended. The suspended list is also common in that it is the list that players who are suspended by their teams or the NFL go on. For example, Darrell Russell will be placed on the Raiders' reserve/suspended list since the NFL suspended him for 16 games. Also the Bears fullback Daimon Shelton will be on this list for the first four games of this season. There are probably others, but I do not know them.
Waivers are nearly a complete mystery to me. I think I understand the basis of it, but I don't think I'll ever fully understand this system. I believe if a player has 3 or less years of NFL service, they can be waived. Otherwise, it is called contract termination. If a player is waived, it is like being cut or released. Except for, that other teams are allowed to put in waiver claims within a 48-hour period (possibly 72 hours though). The team with the worse record that put in one of these claims is awarded the player. For the entire off-season and first few weeks of the season (6-8 I believe), the previous year's records determine the winner of the waiving sweepstakes. Afterwards, it is the team with the weakest record in the current year up until the end of the season. If a player is unclaimed in this 48-72 hour period, then they automatically become "normal" free agents.
Practice squad refers to the list of players that practice with any given team. Teams are allowed to keep up to eight players on this list. Although these players are allowed to practice with and travel with the team, they are not official members of the team. They are free agents, and are allowed to sign and negotiate with any of the other 31 NFL teams. If Team B signs a member of Team A's practice squad, then that player must be signed to Team B's 53-man roster. I do not know the exact wages, but practice squad players do get paid weekly. This salary ranges between $4 and 6,000 typically, but is up to the team to set. But there is a NFL-required minimum I believe. But I do not know this exact figure. The rules that make a player eligible for a practice squad are as follows:
Accrued seasons are ones that count for NFL service. This only matters when determining a player's free agency status, and minimum salaries. The determining factor of an accrued season is six or more games by a player on a team's active or inactive list. A player just needs to spend six weeks on the team's 53-man roster, or on any of the three main reserve lists mentioned above. I do not believe that spending six or more weeks on the other reserve lists mentioned will count for a season.
Injury settlements are basically compensation between a player and a club. NFL rules stipulate that clubs cannot release injured players, much like in real life jobs. Injury settlements occur when an injured player is released. I do not know exactly what happens, but I think it basically is an agreement between the player and club about how much of the player's contract they will receive as part of being released.
Salary Cap Info
You can refer to the FAQ found on this page to find out how much the salary cap applies in training camp.