Scripting testing means you have to write the script in order to execute the test steps.
Example : Selenium Webdriver with any supporting programming language.
The scripting approach is recommended as we will be in complete control over the script. Whenever the application under test web elements change, we can change only that element locator. Anyway you should follow right script design patterns(for example: page object model) to get most out of scripting.
Record and replay testing means, your testing tool will records all your steps and you can play back any time you want.
Example : Coded UI, Selenium IDE(Now it is obsolete, expecting a new version with selenium 4)
Record and playback method is not reliable as change in the web page elements will break the recorded test case.