Does a bitcoin have the same value in every country? Is it not like real money that we use in real life? Does it have a different value in every country?
Your basic assumption that "real money" always has the same value is not really valid. A million dollars is worth a lot more to me than it is to Bill Gates. And it might be worth nothing on a lifeboat in the middle of the ocean.
A Bitcoin behaves like any other commodity. Its value may be different from person to person or area to area based on things like supply and demand.
So long as transaction costs are low, values will be approximately the same under all reasonable conditions because of exchange and arbitrage. Someone who can get a bitcoin for less than other people will sell it to someone willing to pay more, this will take the people willing to sell for less or buy for more out of the market.
Generally, when you find a significant different in the value of a bitcoin in different places, it's explained by some difference in the asset on the other side. For example, at one time, there was a glut of dollars at an exchange called Mt. Gox. This made a dollar at Mt. Gox worth less than a dollar, and bitcoins sold for more of them at Mt. Gox.