"long call: I own the stock, hoping price go up and I profit"
If you buy or sell short an option, you do NOT own the stock.
Options trade separate from stocks. You are confused and have not yet read your first book. Larry McMillan is the options guru if you really want to learn. Any book by him will be instructional.
You can combine them (like anything else, you can combine positions in futures with stocks or futures with options or bonds with stocks, etc), but you're confusing the definitions and creating a separate issue.
There is no reason to buy both the call option and the stock. It's usually one or the other.
A covered call position would be when you buy stock AND sell a call simultaneously.
Options are different from stocks. Your definitions are for stock trading. Not options.
Options contracts are a type of instrument where you're guaranteed a price of a stock (called the strike price) when the contract expires. If it expires or you decide to exercise it early, you're obligated to buy/short the shares at that strike price.
A Long Call is when you buy contracts, thinking that the stock's price will go up and reach the contract's strike price. For example, if you buy Calls for KO with a strike price of $45, you have to make sure that, before the contract expires, the price (currently $39.29) will reach that price. The shorter the expiry, the more risky it is, and the more vulnerable those contracts are to failing.
A Long Put is when you buy contracts, thinking that the stock's price will go down, instead, to reach the strike price. That's like betting on KO reaching $35, before the contracts expire.
A Short Call/Put is basically the opposite. Using margin (like short selling), you short the Call or Put contracts. The key difference is, you wait for the contracts to expire "out-of-the-money"; you don't wait for the stock to reach the strike price. That is, you short contracts betting that people will buy them, but knowing that the stock will never reach that strike price.
For example, those same Call options, with a strike price of $45, are very unlikely to reach that price within, say, two weeks. You can short those particular Call options, and wait for them expire worthless for those buyers. You earn the full market value of those contracts, when they expire worthless for them.
One thing to remember is that, if your contracts expire, regardless of whether they're a profit or a loss, you must exercise them. That means, you can place yourself in debt if you cannot afford the shares. However, some brokerages will allow you to opt out of this problem; you can ask the brokerage to simply let them expire worthless. Some brokerages will even automatically factor in your capital, and do that for you, since they know you can't afford the shares.
I don't really understand the concept of this options
from what I've read,
long call: I own the stock, hoping price go up and I profit
long put: I own the stock, hoping price go down and I profit
short call: I borrow someone's stock, sell it, hoping the price go down and get profit, buy the stock back and return it to the original owner
short put: I borrow someone's stock, sell it, hoping the price up, get profit, and I don't know afterwards. Will you buy the stock at higher price?
Or do I have wrong understanding, can someone give me better explanation? Thanks!