Its confusing and there is a good reason they pay people to know it.
Hard to explain. But let me try piece by piece.
Lets say you have 70 mil in contracts thatvare all non LTIR. And one player that is LTIR at 5 mil. Your cap hit for the team is 75 mil. Lets say there is an 80 mil cap. Youvhave 5 mil in space.
At the trade deadline, you can take on 5 mil in space. At roughly 30% of the season left, you can take on a 16.3 mil player (or combo of players). Technically a little more but lets not go into that. 5 mil / 30% = 16.3 mil.
Now lets say, same scenario, before the season starts, you add in an 8 mil per year cap hit player. Your cap hit is now 83 mil. With an NHL cap of 80 mil. Your teams cap hit becomes 83 mil. This is because your teams cap hit only rises by the amount youre exceeding the cap. (And cant be more than your LTIR total). so yiu cant exceed the cap by more than 5 mil. Butbyour new cap does not become 85 mil.
How is that different? This part is key. If your new cap was 85 mil becausenof the 5 mil LTIR, and youre onlybsoending 83, you would be 2 mil under the cap, and you accumulate that cap spacet. You can use it at the deadline. But your new cap is NOT 85 mil, its only 83 mil. I.e. toure deemed to be at the cap and you dont accumulate any usuable space.
Ita an important difference because it enables contending teams that are inder the cap to pick up elite players on expiring contracts. And its also why players, especially those with expiring contracts, go for a premium at the deadline. (Not necessarily JUST expirimg contracts butbthe following season youre hit with full cap so yiu have to be able to fit the player in).