No problem!
The main difference is that it's literally impossible to win on a compensated slot if you just sit there and spin it through one of its entire pay cycles. It's sort of like scratch tickets. If you bought the entire set of one game from the state, you'd be guaranteed to lose exactly how much they designed that game to generate in revenue. The only way you can win at a compensated game is if you only play during a "hot" period. Back to the scratcher analogy, if you somehow knew that there were more winning tickets than losing tickets left, you would know that that particular scratch game was due to pay out. Most casino games are never "due" for anything, but compensated slots are one exception.
With regard to your other question about non-compensated games, it works because you can mathematically analyze the games to find what they should pay out in the long run. An easy example would be a coin toss game where you win 1:1 if it lands on heads, and lose if it lands on tails. Assuming that it never lands on its side or vanishes into thin air or something, you know you've got a 50% chance of winning and a 50% chance of losing, but there's no guarantee that you'll ever exactly have a 50% win rate. After 100 tosses, for instance, it's possible that you'll only get heads 35 times and tails 65 times. But with more tosses, it'll get closer and closer to 50-50, and eventually so close that any difference is statistically insignificant. Variance is what tells you what range of values you can expect, as well as indicates how long the "long term" is for a particular game.
I don't know much about the RNGs used, but I do know that they're more statistically "real" today than they were a decade ago. My guess is that the people who develop slots make them then run a large simulation to make sure its actual return falls in an acceptable range before releasing the game to the public.