Some differences of PUP vs. IR:
To be on PUP, you have to be placed on it when TC starts. If you have 1 practice, you can no longer be on PUP nor be placed on PUP.
To be placed on IR there are a few factors when to be placed on IR. You can be placed on IR right before the season starts. Even it is an injury less than 6 weeks to recover. And you do not need to be designated to return, like it used to be. The team can use it for any player. Normally a main player if a 4 week injury, just takes up the roster spot. But for a lesser player they could place him on IR.
Also IR can be used during the season. I player gets a 5 week injury, but they do not want to use a roster spot, they can put him on IR then bring him back later.
Where the 6 week injury comes in for IR is in TC. If a player is injured, they just can't put him on IR and bring in another camp body. If so, then teams would have 120 players to pick. and choose for practices. They would need to release that player with an injury settlement to bring in another player.
However if shown that it is a 6 week or longer injury, such as a torn ACL. Then they can go ahead and put them on IR. No they still can release them as in some case they do with an injury settlement as opposed to keeping them on IR all season. A Botton tier guy or just a camp body, you would release. A player like Rico they kept.
Maybe these rules changed in the last year, or I may be slightly off, but that is pretty much how I understand it.