If I really understood it, you bet that a quote/currency/stock market/anything will rise or fall within a period of time.
So, what is the relationship with trading ? I see no trading at all since I don't buy or sell quotes.
You are not betting as in "betting on the outcome of an horse race" where the money of the participants is redistributed to the winners of the bet. You are betting on the price movement of a security. To do that you have to buy/sell the option that will give you the profit or the loss. In your case, you would be buying or selling an option, which is a financial contract. That's trading.
Then, since anyone should have the same technic (call when a currency rises and put when it falls)[...]
How can you know what will be the future rate of exchange of currencies? It's not because the price went up for the last minutes/hours/days/months/years that it will continue like that. Because of that everyone won't have the same strategy. Also, not everyone is using currencies to speculate, there are firms with real needs that affect the market too, like importers and exporters, they will use financial products to protect themselves from Forex rates, not to make profits from them.
[...] how the brokers (websites) can make money ?
The broker (or bank) will either:
- Act like an intermediary and buy the contract from another willing seller and resell it to you by taking a little margin
- Create a contract to give you the gain/loss specified in the contract. Then they can hedge it (fully, partially or not at all) by trying to do the opposite of the contract with a combination of several financial products. When it come to taking risk (ie, without a full hedge), it's more likely to be a bank or an hedge fund not a broker.
I'm really afraid to bet because I think that they can bankrupt at any time! Are my fears correct ?
There is always a probability that a company can go bankrupt. But that's can be very low probability. Brokers are usually not taking risks and are just being intermediaries in financial transactions (but sometime their computer systems have troubles.....), thanks to that, they are not likely to go bankrupt you after you buy your option. Also, they are regulated to insure that they are solid.
Last thing, if you fear losing money, don't trade. If you do trade, only play with money you can afford to lose as you are likely to lose some (maybe all) money in the process.