To understand the difference between derivatives and swaps, first let us understand the similarity.
The one big similarity is that, both are forward contracts. But, the big and the really big difference is on the underlying asset.

If shares of Reliance Industries fall, it is obvious that the derivative, that is the futures price would also fall in tandem. The fall would more or less be in line with the share price of Reliance Industries.
Similarly, with the currency swap. If the rupee falls against the US dollar in the interbank forex market, the futures contract would also move in line with it.
Therefore, a derivative always follows an underlying asset, while in the case of a swap, there is no underlying asset to track.
Now, let us understand the case of an interest rate swap. Let us say that a Financial institution A is borrowing money from an institution B at a floating rate.
They decide that the borrowing rate would be as per the G-Sec rate + 1 per cent. If the G-Sec rate is 6.5 per cent, than institution A would be borrowing at 7.5%.
Now for institution A the interest rate would vary since the G-Sec rate varies. An and when interest rates move, institution A would find its cost of borrowing higher or lower as the case maybe.
Now, if institution B on the other hand is borrowing from institution A at a fixed rate of 7 per cent, they can enter into an interest rate swap.
What would happen is that if institution A, feels that it would not want to take a risk with rising interest rates, it may swap with institution B, which has a fixed interest rate.
This is how swaps work. You could also have currency swapping, which means movement from one currency to another, based on analysis and the ability to take a risk.
Swaps and derivatives both are in vogue
Both are often used these days, through one is an instrument, while the other is not. The basic difference between derivatives and swap would remain the underlying asset. While the former has none, the other has.
For example, gold futures contract (derivatives) would have gold as the underlying asset, while there are derivatives for shares, currency and various other commodities. You need to have through knowledge before you undertake any of the contrats for derivatives or swaps.
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