So then I heard that S=I and I thought oh ok, so savings is sort of a form of spending and therefore it doesn't have a negative effect on the economy. But Then Geerussel(I think) said that actually S!=I or something and now I am VERY confused. Am I mixing up the short run and long run? Does S!=I in the short run but in the long run it does? I'd appreciate it a lot if someone could explain this to me.

Man I really don't get why people make S = I so confusing, but I agree that they do. S = I is literally saying:

Non-consumption Income (a.k.a. total income - income from consumption) = Non-consumption Spending (a.k.a. Investment Spending)

That's an elementary/universal accounting truth (spending = income), with some redefined fancy(confusing) terms. I've never read why the national accounts defines the terms in such a way (such that consumption terms can be cancelled out), but I'm sure they have historical/accounting reasons. Anyway, you see that S / Savings term is referring to "gross savings", which is essentially an income term. It has literally nothing to do with our common-sense notion of 'saving' like choosing to put money in a bank checking/saving account or buying a government bond.

An example: say my neighbor and I are a tiny microcosm economy. I pay her $10 for something, then she pays me $10 for something else (even with the same $10 bill), then I pay her $10 for something else, and on and on like that. Over the course of one week we traded that $10 bill back & forth 200 times. For the sake of simplicity, say all of this activity falls under investment spending and not consumption (they're just categories anyway). So calculated for that week, the total Investment for our economic sector was $2000. And the total Savings for our economic sector was also $2000. Because these are gross flows. Doesn't sound much like colloquial 'savings' or 'investment' does it (and that's probably why these are such confusing terms). Of course there were 0 net spending or saving flows, because that would require outside sectors interacting with us.

Sumner explaining it:

Similarly, saving once had a common sense meaning that was different from investment. Saving and investment (as defined in earlier eras) were not equal by definition. But then economists found it useful to define saving as the funds spent on investment. They became two sides of the same coin, like sales and purchases.

Also I think there are some moral judgments embedded in this stuff: people like the idea that they're actively helping the economy by stashing money away in the bank, and not imprudently just consuming away the country's wealth like some low-class spendthrift. So it's very enticing to hear "S=I" and to mistakenly think "oh I'm investing and contributing to long-run growth! The economy needs more disciplined savers"