This completely depends on the contract of the player involved.
Anyone making 5 million dollars a year will almost assuredly have an injury agreement paying them the full amount if waived or placed on IR - after a certain date in the season (for most start of OTAs or training camp). So that is why you don't see higher priced players being waived - teams have to pay them anyway.
They would rather keep track of their injury and keep a good reputation of player treatment. If they do waive a high price player the player goes through the waiver process. If no other team picks him up he is put on IR.
Why would a team waive a player? For players with lower salaries there is usually no guarantee for injuries. If the team didn't like what they saw, didn't like the attitude of the player, or whatever it may make sense to waive the player because they were going to do it anyway.
So when waiving a player the team has to basically prorate the injury time and pay a player accordingly. The player has to agree to this amount or they go through an arbitration process.
Most younger players basically go into three buckets.
- Team gives them a wink and says we don't want to cut you so maybe your hamstring is really tight... IR time. They get to stash a talent on their team. That player can go to meetings, use facilities and everything all year. This is good for the player because they are getting paid and establishing a good relationship with a team/coach. Bad point here is that some team maybe could have played this player this year.
If that player said no to IR and team put him on practice squad then any team can make him part of their 53 man roster.
Player is considered borderline for the league. They get an injury but not long-term. Instead of milking 2-4 weeks pay out of a team they ask to be waived so they can be picked up by another team. If this player took an injury settlement then other teams might see damaged goods or a guy who is going to milk an injury settlement every time he gets dinged.
This player just isn't good enough to make a team. They should probably take any settlement they can get. They might not want to be around other teams until they are paid since no one can gauge their lack of value without seeing them.
As far as salary cap any waived player released on non-guaranteed contracts (no injury provision) will not count but this is a very small percentage of money in the league because there are almost always provisions in larger contracts.
Even guys with smaller contracts have their contracts guaranteed if they are on the roster for more than 3 weeks (53 man roster) or if they are on a roster after week 6. Why you see some teams bounce a guy and take him back early in the year.