Selenium is just a browser automation tool. It will help you open the browser and imitate the user actions. Selenium support cross browser automation and now even mobile browser and native app automation as well.
Selenide is the framework developed for test automation using Selenium WebDriver. It has very good API to connect with Selenium WebDriver.
eg.
In selenium WebDriver, you write
By username = By.name("username");
driver.findElement(username).click();
In case of Selenide, you can simply write
By username = By.byName("username");
$(username).click();
As you can see, write the code is made very simple.
It has got inbuilt mechanism for WebDriverWait, so waiting for Ajax call is very easy. You can expect stable testing project for an app with Ajax calls.
Hope that helps!
