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I know in American options you can exercise the options at any time before expiry date but in European options you can only exercise the options on expiry day.

On National Stock Exchange of India the options traded are European types but I have closed my option position before expiry. So I am confused between expiry date and exercise date.

Can anyone tell the difference between these two with simple example?

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Exercising an option on some date $t$ means that you receive the payoff of the option $G_t$ on that date. For example, if a call option is exercised you'd get $(S_t - K)^+$ if you exercise on date $t$.

For American options, since you can exercise whenever (as long as expiration has not yet occurred), the chosen date (by the owner of the option) to exercise is called the exercise date. And this date of exercise is on or before the expiration date of the option. For European options the only possible exercise date is the expiration date.

If you close out your option position (by selling it), this is just giving the option a new owner, so all the option properties are still the same. You receive whatever the option price was in the market on the sale date and all the rights/privileges from owning the option goes to the new owner.

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