In the United States, we vote for nationwide office on one day. It's a long day as many polls are open at 6am, close at 9pm and the US spans a number of time zones. (Without looking it up, I believe Hawaii is 6 hours earlier than the East Coast.) There's always complaining by the west coast (and presumably Hawaii/Alaska) that the election is decided before the later people vote. The media responded by delaying "calling the election" until the West Coast closes their polls. Which means even in the last election (which wasn't close in electoral votes), the media didn't say anything until I went to sleep.
In India,the Prime Minister(though President is the Head of State, its just a rubber stamp position,a great waste of money. Also, the present incumbent has no qualities what so ever, but is in place because an Italian lady thought so. The President gets to live in a palatial bungalow, roam about the world at the cost of tax payers money and have fun.) is not elected directly by the electorate. He is the consensus candidate of the party/ies forming the govt. Also, exit polls are banned.
Conducting polls in India is a logistical nightmare. Our neighbours also would love to disrupt the process.
Keeping all this in mind, the poll process is conducted in parts.
And yes, you correctly stated that the counting is done after polling process is completed everywhere.
If I become filthy rich, I'll sponsor research for painless dental treatment at Harvard Medical School. Thats why,I'm learning Java.I have 32 teeth, 22 are man made.