There are hashing calculators in the internet that tells the average amount of bitcoin you'll make in a period of time. I know that when you generate a block you gain 25 BTC (I guess it is still the reward). How is this possible? It's saying you gain ~10000 dollars when you generate a block? The only way to mine bitcoin is either by generating an entire block, which they say will reward you with 25BTC. But the calculators say something like $200/month. How is this possible? For me, the only way to gain is by winning 25BTC + fees of the block, or not gaining anything.
You are correct, bitcoin mining is a very binary thing. Either you find the hash and you get rewarded bitcoins (currently 25 BTC) or somebody else finds it and you get nothing and have to try your luck on the next block. But because solo mining is such a crapshoot, people tend to join their miners together into what is known as a "mining pool". In this way, because a pool of miners has much more processing power than a solo machine, there is a much better chance that it will find a block and get the reward. When this happens, the reward is split amongst everyone who contributed to the pool based on the amount of processing power they contributed. You get much less BTC than if you had found the block yourself, but the rewards are more consistent. Those hashing calculators are never exact because bitcoin mining is, by design, meant to be random. All they can do is make an assumption, probabilistically, of the average amount of BTC you might make based on your hashrate.
The mining reward is assigned to the miner by the very block he finds. This happens in the first transaction in the block, the Coinbase transaction. So, yes, there is only one mining reward given out every block, and it is currently 25BTC + fees.
As finding a block is a rare event, miners organize in mining pools. They pool their work, but then also share the revenue. That way, the time between finding blocks is shortened, and payouts are more frequent but smaller. Mining pools buffer miners from the variance of solo mining.