What are the differences between hedging with swaps, options or futures? For instance if a bank wants to hedge against interest rate risk, it could use interest rate swaps, or options or futures contract. Or in any other example, when a manager is hedging against risks.

Can somebody show it how these differ from each other in an example?
The scope of this question is quite large. There are a lot of ways of hedging interest rate risk. Note that there is a quantitative finance stack exchange, and this question might fit better there.

All rates instruments have a sensitivity to interest rate changes. That is, their value goes up or down in response to interest rate movements.

If we assume that all interest rates move together in parallel (that is, spreads are unchanged), all you need to do to hedge interest rate risk is find instruments that have a value change that cancels the risk you want to hedge.

To a certain extent, most non-credit rates are correlated, and so one can use a wide variety of instruments to hedge.

However, rate movements are not perfectly correlated. As such, hedges may need to be structured to have a sensitivity closer to the risk to be hedged. How that is done is the full time job of interest rate traders. That is, too large a scope to be ansered in a single question here.