What is the difference between WebDriver.close() and WebDriver.quit()

WebDriver.close() method closes the current window.

See the below example, here it opens the new link in a different window and upon executing the close() method, it closes the parent window and leaving the new window open.

WebDriver driver=new FirefoxDriver();
driver.get("http://google.com");
driver.manage().window().maximize();
WebElement oWE=driver.findElement(By.linkText("About Google"));
Actions oAction=new Actions(driver);
oAction.moveToElement(oWE);
oAction.contextClick(oWE).sendKeys(Keys.ARROW_DOWN).sendKeys(Keys.ARROW_DOWN).sendKeys(Keys.ENTER).build().perform();
driver.close();

Whereas, WebDriver.quit() method quits the driver, and closing every associated window.
In the above example, if you use driver.quit() in place of close , then first opens "google" page and then open the "about google" in new window and closes both the windows.

How to check the object existance

Here in the below code, i am checking for an object existence.

    //Max_TimeOut variable holds the time in seconds for the maximum time to wait before the control flows to NoSuchElementException block.
    int Max_TimeOut=60;
    public boolean isObjExists(WebDriver driver,By locator)
    {
        //I am putting the code in try catch because if the object does not exist, it throws exception.
        try
        {
            //Before throwing exception, it will wait for the Max_timeout specified
            WebDriverWait wait=new WebDriverWait(driver,Max_TimeOut);
            wait.until(ExpectedConditions.elementToBeClickable(locator));
            //If the element found, then it returns true
            return true;
        }
        catch(NoSuchElementException exception)
        {
            //If the element is not found, then it returns false
            return false;
        }
       
    }

This function can be invoked in like below:
        By locator=By.name("Email");
        if(obj.isObjExists(driver, locator))
        {
            Reporter.log("Object exists");
            WebElement uNameElement=driver.findElement(locator);
            uNameElement.sendKeys("abcd");
        }
        else
        {
            Reporter.log("Object does not exist");
        }