Contradictory statements in the Varsity options module

F&O
1

Statement 1. :-European Options – If the option type is European then it means that the option buyer will have to mandatory wait till the expiry date to exercise his right. The settlement is based on the value of spot market on expiry day.So all options in India are now European in nature , which means the buyer can exercise his option based on the spot price on the expiry day.

Statement 2 :-For example, if I have bought Bajaj Auto 2050 call option at Rs.6.35 in the morning and by noon the same is trading at Rs.9/- I can choose to sell and book profits.

My question is, if one can sell it just half an hour later,how come it is a European option?
Also, can an option seller also square off his position one or two hours/days prior to expiry if he watches position going against him ?

2

Exiting and exercising options are different things.
The first is akin to buying a plot and then selling it later.
While 2nd option is like building a house over a plot.
Please read a chapter on OI for clarification

3

@nashtrik
When you exercise a Long option position (call or put), you only get the payoff with respect to that days underlying closing price. But when you sell it off, you also get the benefit of Time value of the option.
Read more with an example here:

and another one to check for example: