Most of the time it makes more sense to sell the option rather than exercise the it and then have to close the position in the underlying. The reason for this is that the option may have some salvageable time premium and you'll incur fewer commissions.
If an option is one cent or more ITM at expiration, the OCC will automatically exercise your options whether they are long and short (Exercise by Exception). For equity options, you will end up with a position in the underlying (index options are cash settled and they have other issues). If you are long the option, you can designate to your broker that your options not be exercised at expiration. This would make sense if they are ITM by pennies and your commission to close exceeds that..
Where it makes sense to exercise and then buy/sell the stock is if you own an ITM option and the bid trades below parity (less than intrinsic value). By selling at the bid, you'll take a haircut. This makes sense if commission total is less than the haircut. Speaking of which, paying $7.70 for one option contract is highway robbery (nearly 20% of the option's cost).
As an example, IBM is currently $138.75 and the June 29th $150 put has a bid of $10.80. The intrinsic value of the put is $11.25 but the best bid is only $10.80 (most likely the market maker) so that's a 45 cent haircut. You could place an order for a better closing price but you are not likely to get full intrinsic value because there's no incentive for anyone to do so.
If you were to sell your put for $10.80, the market maker would immediately do a discount arbitrage. He'd exercise the put to sell the stock at $150, while simultaneously buying the stock for $138.75 to close the position. The net gain would be 45 cents ( - $10.80 - $138.75 + $150.00).
Assuming you have the funds in your account, you can do this yourself. Where I trade, equity is commission is 50 cents per 100 shares with a minimum ticket of $1. Assignment and exercise are free so my cost to do this on 100 shares would be $1. For 200 or more shares, my cost to do this would be 50 cents per hundred shares in order to save as much as $45 per contract. More realistically, it might be $5 or $10 or $15 but the savings is still significant, particularly when you own a number of contracts.
So no, you don not have to buy Intel stock when closing the position unless the OCC is dealing with an ITM option at expiration and you failed to designate 'Do Not Exercise". But as explained above, you might want to. And no, e*trade will never just give you the difference between the strike/actual prices minus any fees.