In Islam I heard that same thing can't be exchange with profit or loss. Now I'm curious to know about currency/money exchanging is permissible or not in Islam?
Allah knows best, but in my opinion, it depends on the context.
If you are exchanging to gamble and try your luck in gaining a profit from the various rates during the day or week, then it is definitely haram.
If you are exchanging to go to a different country where you can only spend in their local currency, then it is a necessity and hence not haram.
If you are exchanging in a trading environment where you may incur a profit or loss on exchange, even if you meant for it to be so via forward trading, then I'd say it is not haram, since Islam does allow trading for a profit.
Essentially, a Dollar and Pound is not the same thing. The Dollar is a legal tender backed by the central bank of the USA and the Pound is backed by the Queen(or UK Bank?). They have different purchasing power and hence are not on a 1:1 exchange rate.
The other way to look at this is that whatever is not explicitly forbidden is Halal, and in terms of Finance, only Usury and Interest are haram as far as I know.
❶ - Are you speaking about different currencies? You cannot exchange the same currency (like gold) for different amounts, as that is riba (taking more for less, when it is the same currency).
❷ - But if you are speaking of exchange of gold for silver, and so on, then of course the amounts will differ based on the value being different.
Proof for both of the above points are available in the hadith below:
قَالَ أَبُو بَكْرَةَ ـ رضى الله عنه ـ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم " لاَ تَبِيعُوا الذَّهَبَ بِالذَّهَبِ إِلاَّ سَوَاءً بِسَوَاءٍ، وَالْفِضَّةَ بِالْفِضَّةِ إِلاَّ سَوَاءً بِسَوَاءٍ، وَبِيعُوا الذَّهَبَ بِالْفِضَّةِ وَالْفِضَّةَ بِالذَّهَبِ كَيْفَ شِئْتُمْ " - Narrated Abu Bakra: Allah's Messenger (ﷺ) said, "Don't sell gold for gold unless equal in weight, nor silver for silver unless equal in weight, but you could sell gold for silver or silver for gold as you like." (Bukhari).
It is, because all islam countries have national banks which keep some foreign currency reserves. Also most of the islam countries have normal exchanges for tourists. And they must have it right, otherwise Allah would stop it - he is all powerful.