PoS1 means that people are receiving free internet money without doing any work that is useful for our coin (just for holding it), as they just need to open and close their wallet sometimes.
PoS2 means that to make money they'd provide nodes to SLM, which we need for a better connectivity.
To clarify this "PoS version salad"
What's called "PoS1" frecuently is the original Peercoin PoS. In this variant, the reward of a stake is limited to a fixed percentage of it per year. In PPC it's 1%, in SLM, it's 10% of the stake. This means that as long as you find a block with a stake once in a year (or once in 90 days? I'm currently in doubt ...) at least, you will get your maximum reward. So if you want to maximize reward, it's not necessary to stay online with the client. (So yes, what you write is correct - you have to open your client and stake only once in a while. However, if you don't find a block e.g. because your stake is too small, you won't get reward.)
Blackcoin introduced two new versions they called "PoS2" and "PoS3". In these variants, coin age is no longer used to calculate rewards, nor the probability to find blocks - only the pure coin holdings. See:
https://www.rstr.io/files/pos2.pdf. "PoS2" is also pretty similar to the PoS used in NXT. It is basically the "most simple PoS protocol possible", so it's a bit ironic they call it "PoS2".
The advantage (for network security) is that nodes have to stay always online to get maximum rewards. The disadvantage, however, is that PoS2 is more vulnerable to
nothing at stake attacks, because in the case of a blockchain fork people will get more rewards if they try to stake on all forks. These NaS attacks are difficult to perform but theoretically devastating. Peercoin in PPC0.5 (or 0.6?) introduced a change where coin age was taken out for the probability to find blocks, but stays there for the reward calculation. This combines advantages of both approaches.
Peercoin 0.9's changes are not the same Blackcoin introduced. In fact, the system is more similar to "PoS1", because rewards are still limited to ~1%/stake per year. The change is that the reward can increase to more than 1% temporarily if the PoS rewards over a longer time have not reached the 1% mark. This can happen if a significant percentage of Peercoin holders do not stake. The system thus approaches a constant 1% inflation. The goal is obviously to incentive staking participation, as was the goal for PoS2. But the technique used is different, and is less vulnerable to nothing-at-stake.